energies

Article A Two-Way Neutronics/Thermal-Hydraulics Coupling Analysis Method for Fusion Blankets and Its Application to CFETR

Tao Dai 1, Liangzhi Cao 1,* , Qingming He 1, Hongchun Wu 1 and Wei Shen 1,2

1 School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China; [email protected] (T.D.); [email protected] (Q.H.); [email protected] (H.W.); [email protected] (W.S.) 2 CANDU Owners Group, Toronto, ON M5G 2K4, Canada * Correspondence: [email protected]



Received: 16 July 2020; Accepted: 4 August 2020; Published: 6 August 2020


Abstract: The China Fusion Engineering Test Reactor (CFETR) is a tokamak device to validate and demonstrate fusion engineering technology. In CFETR, the breeding blanket is a vital important component that is closely related to the performance and safety of the fusion reactor. Neutronics/thermal-hydraulics (N/TH) coupling effect is significant in the numerical analysis of the fission reactor. However, in the numerical analysis of the fusion reactor, the existing coupling code system mostly adopts the one-way coupling method. The ignorance of the two-way N/TH coupling effect would lead to inaccurate results. In this paper, the MCNP/FLUENT code system is developed based on the 3D-1D-2D hybrid coupling method. The one-way and two-way N/TH coupling calculations for two typical blanket concepts, the helium-cooled solid breeder (HCSB) blanket and the water-cooled ceramic breeder (WCCB) blanket, are carried out to study the two-way N/TH coupling effect in CFETR. The numerical results show that, compared with the results from the one-way N/TH coupling calculation, the tritium breeding ration (TBR) calculated with the two-way N/TH calculation decreases by 0.11% and increases by 4.45% for the HCSB and WCCB blankets, − respectively. The maximum temperature increases by 1 ◦C and 29 ◦C for the HCSB and WCCB blankets, respectively.

Keywords: CFETR; fusion blanket; Neutronics/thermal-hydraulics Coupling

1. Introduction In order to validate the science feasibility and demonstrate the engineering technology of the magnetic-confinement fusion reactor, and achieve the transition from experimental device to demonstration reactor (DEMO), the China Fusion Engineering Test Reactor (CFETR) was proposed by the China National Integration Design Group [1]. One of the most challenging tasks is to realize tritium self-sufficiency, which mainly depends on the design of the breeding blanket. To achieve the design goal of tritium breeding, energy extraction, and radiation shielding, the blanket design is significant to the performance and the safety of the CFETR. Blanket design involves many scientific fields. The most relevant fields include neutronics and thermal-hydraulics [2–14], which will directly influence the operation of the fusion reactor. In the early stage, blanket design works were performed independently without considering the coupling effects among different fields. With the advances of the blanket design, the demand for high-precision numerical analysis of the blanket is growing and the integrated approach to the blanket design is getting more attractions. Utoh [15] developed a 2D nuclear/thermal coupling analysis code DOHEAT.

Energies 2020, 13, 4070; doi:10.3390/en13164070 www.mdpi.com/journal/energies Energies 2020, 13, 4070 2 of 20

This code adopts DOT3.5 as the 2D SN transport module, APPLE-3 as the neutronics calculation module, and a 2D steady-state heat transfer module. It was used in various Japanese blanket conceptual designs. Spagnuolo [16] developed an integrated blanket design code system MCNP/ANSYS for neutronics, thermal-hydraulics, and the mechanics design of the blanket. The code system was applied in the water-cooled lithium lead blanket (WCLL) and the helium-cooled pebble bed blanket (HCPB) for the European DEMO project. Jiang [17] and Cui [18,19] developed multi-physics integrated optimization and design platforms based on MCNP and ANSYS for the water-cooled ceramic breeder blanket (WCCB) and the helium-cooled solid breeder blanket (HCSB) of CFETR, respectively. In their work, they focus the most attention on the individual neutronics calculation or thermal-hydraulics calculation, thus the one-way coupling method was adopted. The one-way coupling method means that each solver runs only once and the feedback effects between the neutronics and thermal-hydraulics calculations are not taken into account. In reality, there is an interaction between neutronics and thermal-hydraulics. The variation of the thermal-hydraulics parameters, including the material temperature and the coolant density, will lead to the variation of the neutronics parameters like TBR and nuclear heat deposition, which will then impact the thermal-hydraulic parameters in turn. The two-way N/TH coupling calculation has proven to be necessary in the numerical analysis of the traditional fission reactors. However, the influences of the two-way N/TH coupling effect in the fusion blanket are still unclear. To quantify the influences of the two-way N/TH coupling effect in the fusion reactor and obtain more accurate and reliable design parameters for CFETR, the two-way N/TH coupling method should be studied. In this paper, the coupling neutron/photon continuous-energy Monte-Carlo code MCNP and the Computational Fluid Dynamics (CFD) code FLUENT are adopted to develop the two-way N/TH coupling code system. Considering there are a number of blankets and the blanket structure is extremely complicated, a 3D-1D-2D coupling method [20] is used to reduce the difficulty in modeling. Moreover, the pseudo-material method [21] is adopted to obtain neutron cross sections at the arbitrary temperature. Based on these methods, the two-way N/TH coupling effect in two main conceptual blanket design of CFETR, HCSB, and WCCB, are studied. This paper is organized as follows. In Section2, the two-way N /TH coupling method and the models of the HCSB blanket and the WCCB blanket are introduced. Section3 presents numerical analyses including sensitivity analysis of temperature and the comparison between the results of one-way and two-way N/TH coupling calculations for the HCSB blanket and the WCCB blanket. Finally, the conclusions are given in Section4.

2. Coupling Method and Blankets Models

2.1. The Two-Way N/TH Coupling Method Generally, the N/TH coupling code system consists of two codes, neutronics solver and thermal-hydraulics solver. Many N/TH coupling codes have been developed based on different neutronics codes and thermal-hydraulics codes [22–25]. In the International Thermonuclear Experiment Reactor (ITER) project [26], neutronics code MCNP and CFD code CFX/FLUENT are appointed as the official design tools. Therefore, MCNP and FLUENT are adopted to develop the two-way N/TH coupling code system and carry out the N/TH coupling calculation in this work. Because of the thermal motion of the nucleus, neutron cross sections will be changed at different temperatures. However, the FENDL/MC-2.1, an ACE-format nuclear data library for the Monte-Carlo simulation of fusion reactor, only provides the cross sections at room temperature. Hence, the multi-temperature cross sections should be generated in the coupling process. Considering the generation of the cross sections at a specific temperature on-the-fly based on the Doppler-broadening theory will cost huge time, the pseudo-material method is adopted to generate the cross sections. The pseudo-material method is an interpolation method to generate cross sections at a temperature T between two temperature points, TL and TH, the low temperature and the high temperature. The cross Energies 2020, 13, 4070 3 of 20

Energies 2020, 13, x FOR PEER REVIEW 3 of 22 sections at TL and TH have been generated ahead. An atomic-density fraction is computed based on linear interpolation between the square root of the low temperature and the square root of the − high temperature: TTH f = . (1) T √TH − √T fT = TTHL− . (1) √TH √TL − Then, the cross sections at temperature T could be calculated by mixingmixing cross sections at low temperature with a fraction of f and cross sections at high temperature with a fraction of (1−f ) . temperature with a fraction of fTT and cross sections at high temperature with a fraction of (1 fTT ). − ThisThis isis realizedrealized byby changingchanging thethe atomicatomic densitydensity ofof thethe materialmaterial inin thethe MCNPMCNP materialmaterial card.card. Considering the blanket structure is complicated andand the heterogeneous eeffectffect isis strong, the time spent onon blanketblanket modelingmodeling andand data data transmission transmission between between neutronics neutronics and and thermal-hydraulics thermal-hydraulics codes codes is longis long in in the the 3D 3D N /N/THTH coupling coupling calculation. calculation. In In the the neutronics neutronics calculation, calculation, the the 3D-1D 3D-1D hybrid hybrid method method is provedis proved eff ectiveeffective and and time-saving. time-saving. In the In thermal-hydraulicsthe thermal-hydraulics calculation, calculation, although although the 3D the model 3D model could providecould provide more accurate more accurate results, results, it will cost it will huge cost human huge work human on modelingwork on modeling and computational and computational resources. Consideringresources. Considering that the layers that layout the layers in HCSB layout and in WCCB, HCSB andand the WCCB, coolant and flows the mainlycoolant in flows two directions,mainly in thetwo 2D directions, model is suitablethe 2D model to perform is suitable the thermal-hydraulics to perform the thermal-hydraulics calculation. Therefore, calculation. instead ofTherefore, carrying outinstead 3D couplingof carrying calculation out 3D coupling directly, thecalculation 3D-1D-2D di hybridrectly, the coupling 3D-1D-2D method hybrid is employed coupling to method improve is theemployed calculation to improve efficiency the andcalculatio feasibilityn efficiency of the Nand/TH feasibility coupling. of Thethe N/TH flow chart coupling. of this The procedure flow chart is shownof this procedure in Figure1 .is shown in Figure 1.

START

Run MCNP with the detailed 3D neutronics model, output the NWL

Build the 1D cylinder model for MCNP and 2D model for FLUENT

Run MCNP with the 1D neutronics model, calculate the power density according to the Update MCNP input card tally results and NWL according to the material temperature and coolant Run FLUENT with the 2D density thermal-hydraulics model, output the temperature and coolant density fields

NO Are the TBR and power density convergent?

YES

END

Figure 1. Flow chart of the two-way MCNPMCNP/FLUENT/FLUENT coupling code system.

Firstly, to acquire accurate neutron flux distribution in different blankets, the 3D CFETR model, Firstly, to acquire accurate neutron flux distribution in different blankets, the 3D CFETR model, which contains all blankets with different dimension sizes, in-vessel components and the detailed which contains all blankets with different dimension sizes, in-vessel components and the detailed neutron-source distribution is built to perform a neutronics calculation. The Neutron Wall Loading neutron-source distribution is built to perform a neutronics calculation. The Neutron Wall Loading (NWL) obtained from the surface-tally functionality of the MCNP in 3D neutronics calculation (NWL) obtained from the surface-tally functionality of the MCNP in 3D neutronics calculation with FENDL/MC-2.1 is utilized to normalize the actual power. The NWL is kept constant in the following iterations.

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Energies 2020, 13, x FOR PEER REVIEW 4 of 22 with FENDL/MC-2.1 is utilized to normalize the actual power. The NWL is kept constant in the followingSecondly, iterations. in Figure 2, a simplified 1D cylinder model is built to obtain the radial nuclear heat powerSecondly, density indistribution. Figure2, a simplifiedThis model 1D is cylindercomposed model of two is builtannuli, to obtainwhich therepresent radial nuclearfor inboard heat blanketpower densityand outboard distribution. blanket, This respectively. model is composed After fin ofishing two annuli, the 1D which neutronics represent calculation, for inboard theblanket radial nuclearand outboard heat power blanket, density respectively. distribution After could finishing be computed the 1D using neutronics NWL calculation,and nuclear theheat radial distribution nuclear talliedheat power by the density F6 card distribution of MCNP: could be computed using NWL and nuclear heat distribution tallied by the F6 card of MCNP: NAT×× p = N A T , p = ×× × ,(2) (2) EVE V × wherewhere pp isis the the power power density density (W/m (W/m33),), NN isis the the neutron neutron wall wall loading loading (MW/m (MW/m22),), AA isis the the area area of of the the first first wallwall (FW) (FW) facing facing the the plasma plasma (m (m22),), TT isis the the tally tally result result in in the the MCNP, MCNP, which which represents represents the the nuclear nuclear heat heat depositiondeposition (eV) (eV) of the cell, E isis thethe energyenergy ofof thethe fusion fusion neutron neutron (MeV), (MeV), and andV Vrepresents represents the the volume volume of ofmaterial material zones zones (m (m3).3).

FigureFigure 2. 2. 1D1D cylinder cylinder blanket blanket model. model. Thirdly, the 2D model contains the main radial materials layers and the coolant channels are built Thirdly, the 2D model contains the main radial materials layers and the coolant channels are for the CFD calculation. The radial schemes in the 2D model is the same as that of the 1D cylinder built for the CFD calculation. The radial schemes in the 2D model is the same as that of the 1D cylinder model. The 2D model is extended along the poloidal direction. To exchange required data including model. The 2D model is extended along the poloidal direction. To exchange required data including power density, temperature, and coolant density between MCNP and FLUENT, the zones in the power density, temperature, and coolant density between MCNP and FLUENT, the zones in the thermal-hydraulics model are divided the same as the cells in the 1D neutronics model in the radial thermal-hydraulics model are divided the same as the cells in the 1D neutronics model in the radial direction. Once the neutronics calculation is completed, the nuclear heat power density of each cell direction. Once the neutronics calculation is completed, the nuclear heat power density of each cell could be calculated according to Equation (2) and assigned as the heat source of its corresponding zone could be calculated according to Equation (2) and assigned as the heat source of its corresponding in the CFD model. After the CFD calculation is completed, the temperature distribution is obtained zone in the CFD model. After the CFD calculation is completed, the temperature distribution is and is compared with that of the previous iteration. If the maximum difference is smaller than the obtained and is compared with that of the previous iteration. If the maximum difference is smaller convergence criteria, the coupling procedure is ended. Otherwise, the density information and the than the convergence criteria, the coupling procedure is ended. Otherwise, the density information material in the MCNP input file will be updated according to the volume-averaged temperature of and the material in the MCNP input file will be updated according to the volume-averaged each cell and the iteration continues until convergence. temperature of each cell and the iteration continues until convergence. 2.2. HCSB Blanket Model 2.2. HCSB Blanket Model The concept of the HCSB blanket [27] was proposed by the University of Science and Technology of ChinaThe concept (USTC) of for the CFETR. HCSB blanket Typical [27] outboard was propos blanketed moduleby the University structure of on Science the equatorial and Technology is shown ofin China Figure (USTC)3. The toroidalfor CFETR. widths Typical of the outboard FW and blanket the back module plate (BP)structure of the on blanket the equatorial are 1448 is mm shown and in1606 Figure mm, 3. respectively. The toroidal The widths radial of and the poloidalFW and thicknessesthe back plate of the (BP) typical of the blanket blanket module are 1448 are mm 800 and mm 1606and mm, 960 mm, respectively. respectively. The radial A typical and blanketpoloidal module thicknesses mainly of the includes typical tungsten blanket module armor, FW,are 800 top mm and and 960 mm, respectively. A typical blanket module mainly includes tungsten armor, FW, top and bottom caps, stiffing plate (SP), cooling plate (CP), breeder zone (BZ), neutron multiplier zone (MZ), manifolds, and BP. The FW is a U-shape plate and a layer with a thickness of 2 mm of tungsten covers

Energies 2020, 13, 4070 5 of 20 bottom caps, stiffing plate (SP), cooling plate (CP), breeder zone (BZ), neutron multiplier zone (MZ), manifolds,Energies 2020 and, 13 BP., x FOR The PEER FW REVIEW is a U-shape plate and a layer with a thickness of 2 mm of tungsten5 of 22 covers on it facing plasma directly. Forty-five parallel radial-toroidal-radial channels are uniformly set in the FWon it structure facing plasma material. directly. Helium Forty-five flows parallel through radial-toroidal-radial these channels and channels takes awayare uniformly the heat set flux in from the plasmathe FW andstructure the neutron material. heat Helium deposition. flows through The FW, these top channels and bottom and takes caps, away and the BP heat construct flux from a closed blanketthe plasma box, in and which the neutron 7 SPs are heat welded deposition. to the The internal FW, top and walls bottom of the caps, FW and to enhanceBP construct the a mechanicalclosed blanket box, in which 7 SPs are welded to the internal walls of the FW to enhance the mechanical property in the loss-of-coolant-accident (LOCA). Moreover, the SPs divide the blanket module into property in the loss-of-coolant-accident (LOCA). Moreover, the SPs divide the blanket module into 8 8 equal breeding units (BUs) with a height of 106 mm in the poloidal direction. The breeder zones equal breeding units (BUs) with a height of 106 mm in the poloidal direction. The breeder zones and and the neutron multiplier multiplier zones zones are are separately separately assi assignedgned in the in theBU BUin turns. in turns. The TheCPs CPsare arranged are arranged betweenbetween the BZthe andBZ and the the MZ MZ to removeto remove the the neutron neutro heatn heat deposition deposition from from those those zones.zones. The coolant flow directionsflow directions in two adjacent in two adjacent CPs are CPs opposite are opposite to flatten to flatten the toroidalthe toroidal temperature temperature distribution. distribution. TheThe main dimensionsmain dimensions are listed are in listed Table in1 andTable the 1 and materials the mate ofrials di ff oferent different parts parts are are listed listed in Tablein Table2. 2.

FigureFigure 3. Schematic 3. Schematic view view of of the the typical typical Helium-Cooled Solid Solid Breeder Breeder (HCSB) (HCSB) blanket blanket module. module. Table 1. Dimensions of the main parts of the typical HCSB outboard blanket module. Table 1. Dimensions of the main parts of the typical HCSB outboard blanket module.

ItemsItems Parameters Parameters BlanketBlanket size size Poloidal Poloidal height: 960 960 mm; mm; toroidal toroidal width: width: 1448–1606 1448–1606 mm; radial mm;radial thickness: thickness: 800 mm800 mm TungstenTungsten armor armor 2 mm 2 mm FWFW Thickness: Thickness: 28 mm; mm; channel: channel: U-shaped, U-shaped, cross cross section: section: 15 mm 15 ×mm 15 mm,15 pitch: mm, 20 pitch: mm 20 mm × PebblePebble bed: bed: radial thickness: thickness: 20/15/180/30/200/45/40 20/15/180/30/200/45 mm;/40 mm; poloidal poloidal height: height: 106 mm 106 mm BU BU CPs:CPs: U-shaped, U-shaped, thickness thickness 5 mm 5 mm Channel:Channel: cross cross section section 6.1 6.1mm mm × 2.6 mm,2.6 mm,pitch: pitch:10.1 mm 10.1 mm Cap Thickness: 28 mm; channel: W-shaped, cross section:× 6.5 mm × 4 mm, pitch: 14.5 mm Cap Thickness: 28 mm; channel: W-shaped, cross section: 6.5 mm 4 mm, pitch: 14.5 mm SP Thickness: 8 mm; channel: W-shaped, cross section: 6.5 mm × 4 mm,× pitch: 14.5 mm SP Thickness: 8 mm; channel: W-shaped, cross section: 6.5 mm 4 mm, pitch: 14.5 mm BP Thickness: 35/10/10/10/40 mm × BP Thickness: 35/10/10/10/40 mm

Table 2. Material selections of the HCSB blanket. Table 2. Material selections of the HCSB blanket. Parts Material Structure PartsReduced activation ferritic/martensitic Material (RAFM) steel material Structure material Reduced activation ferritic/martensitic (RAFM) steel Lithium ceramic of Li4SiO4 with the 6Li enrichment to be 90% in form of pebbles with a Tritium breeder Lithium ceramic of Li SiO with the 6Li enrichment to be 90% in form of pebbles Tritium breeder 4 packing4 factor of 62% Neutron with a packing factor of 62% Beryllium pebbles with a packing factor of 80% Neutronmultiplier multiplier Beryllium pebbles with a packing factor of 80% Coolant Helium Helium gas with gas a with pressure a pressure of 8 MPa of 8 MPa Purge gas gas Helium Helium gas with gas a with pressure a pressure of 0.12 MPa of 0.12 MPa

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EnergiesReferring 20202020,, 1313,, 4070x to FOR literature PEER REVIEW [28], the detailed 3D neutronics model for the HCSB blanket is shown6 of in 2022 Figure 4, and NWL of each blanket is shown in Figure 5. The equatorial outboard blanket (#12), of Referring to literature [28],2 the detailed 3D neutronics model for the HCSB blanket is shown in whichReferring the NWL to literature(0.47 MW/m [28],) theis maximum detailed 3D in neutronicsall blankets, model is selected for the to HCSB perform blanket the iscoupling shown Figure 4, and NWL of each blanket is shown in Figure 5. The equatorial outboard blanket (#12), of incalculation. Figure4, andIn the NWL 1D ofcylinder each blanket neutronics is shown model, in the Figure radial5. Theschemes equatorial of both outboard inboard blanket and outboard (#12), which the NWL (0.47 MW/m2) is maximum in all blankets, is selected to perform the coupling ofblanket which are the assumed NWL (0.47 to be MW the/m same2) is maximumas that of blan in allket blankets, #12. Figure is selected 6 shows to the perform radial thelayout coupling of the calculation. In the 1D cylinder neutronics model, the radial schemes of both inboard and outboard calculation.neutronics model In the of 1D the cylinder HCSB blanket. neutronics model, the radial schemes of both inboard and outboard blanket are assumed to be the same as that of blanket #12. Figure 6 shows the radial layout of the blanket are assumed to be the same as that of blanket #12. Figure6 shows the radial layout of the neutronics model of the HCSB blanket. neutronics model of the HCSB blanket.

Figure 4. China Fusion Engineering Test Reactor (CFETR) with the detailed HCSB neutronics

Figure 4. China Fusion Engineering Test Reactormodel. (CFETR) with the detailed HCSB neutronics model. Figure 4. China Fusion Engineering Test Reactor (CFETR) with the detailed HCSB neutronics model.

Figure 5. Neutron Wall Loading (NWL) on each HCSB blanket.

Figure7 shows theFigure main 5. flows Neutron scheme Wall of Loading the helium (NWL) coolant. on each To HCSB cool theblanket. HCSB blanket, the helium coolant is firstly pumped into the manifold #1 and distributed into the FW channels. After cooling the FW, the helium is gathered in the manifold #2 and flows into the top cap, bottom cap, and SP parallel. Then, the helium flows into the manifold #3 and is distributed into six CPs. To flatten the temperature distribution on the blanket, the flow directions in neighboring CPs are straggled. The helium flow directions in CPs are shown in Figure8. Finally, the helium is collected in the the manifold #4 and flows out.

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Energies 2020, 13, 4070 7 of 20 Energies 2020, 13, x FOR PEER REVIEW 7 of 22

Figure 6. Radial layout of the 1D HCSB neutronics model.

Figure 7 shows the mainFigure flows 6. Radial scheme layout of of the the he 1Dlium HCSB coolant. neutronics To model.cool the HCSB blanket, the helium coolant is firstly pumped into the manifold #1 and distributed into the FW channels. After coolingFigure the FW, 7 theshows helium the ismain gathered flows inscheme the manifo of theld #2he liumand flows coolant. into To the cool top cap,the HCSB bottom blanket, cap, and the SPhelium parallel. coolant Then, theis firstly helium pumped flows into into the the manifold manifold #3 #1 and and is distributed into sixthe CPs. FW Tochannels. flatten theAfter temperaturecooling the distribution FW, the helium on the is gathered blanket, inthe the flow manifo directionsld #2 and in flowsneighboring into the CPs top cap,are straggled. bottom cap, The and heliumSP parallel. flow directionsThen, the heliumin CPs flowsare shown into the in manifold Figure 8. #3 Finally, and is distributedthe helium into is collected six CPs. Toin flattenthe the the manifoldtemperature #4 and distribution flows out. on the blanket, the flow directions in neighboring CPs are straggled. The helium flow directions in CPs are shown in Figure 8. Finally, the helium is collected in the the manifold #4 and flows out.FigureFigure 6.6. RadialRadial layoutlayout ofof thethe 1D1D HCSBHCSB neutronicsneutronics model.model.

Figure 7 shows the main flows scheme of the helium coolant. To cool the HCSB blanket, the helium coolant is firstly pumped into the manifold #1 and distributed into the FW channels. After cooling the FW, the helium is gathered in the manifold #2 and flows into the top cap, bottom cap, and SP parallel. Then, the helium flows into the manifold #3 and is distributed into six CPs. To flatten the temperature distribution on the blanket, the flow directions in neighboring CPs are straggled. The helium flow directions in CPs are shown in Figure 8. Finally, the helium is collected in the the manifold #4 and flows out.

Figure 7. Flow scheme of the helium coolant. Figure 7. Flow scheme of the helium coolant. Figure 7. Flow scheme of the helium coolant.

Figure 7. Flow scheme of the helium coolant.

Figure 8. Helium flow direction in the Cooling Plates (CPs). Figure 8. Helium flow direction in the Cooling Plates (CPs).

Considering there are layer structures along the radial direction, it is reasonable to use the 2D Figure 8. Helium flow direction in the Cooling Plates (CPs). model in the thermal-hydraulics calculation. Because the FW and BU occupy the most of the volume, the thermal performance of the blanket is largely determined by the FW and BU. Therefore, only the FW and BU are considered in the 2D thermal-hydraulics model. The other parts such as SPs and manifolds are ignored with a constant temperature in the neutronics calculation. A uniform surface heat flux of 0.3 MW/m2 from the plasma is applied as the FW boundary condition. The turbulent model is very critical to the TH analysis, however, the choice of the turbulent model is out of the scope of this paper. Although different models will lead to obvious different temperatures increasing, it does not

influence the nature of the N/TH coupling effect. To simulate the turbulence, after careful comparison Figure 8. Helium flow direction in the Cooling Plates (CPs).

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Considering there are layer structures along the radial direction, it is reasonable to use the 2D model in the thermal-hydraulics calculation. Because the FW and BU occupy the most of the volume, the thermal performance of the blanket is largely determined by the FW and BU. Therefore, only the FW and BU are considered in the 2D thermal-hydraulics model. The other parts such as SPs and manifolds are ignored with a constant temperature in the neutronics calculation. A uniform surface heat flux of 0.3 MW/m2 from the plasma is applied as the FW boundary condition. The turbulent model is very critical to the TH analysis, however, the choice of the turbulent model is out of the Energiesscope2020 of this, 13, paper. 4070 Although different models will lead to obvious different temperatures increasing,8 of 20 it does not influence the nature of the N/TH coupling effect. To simulate the turbulence, after careful −ω andcomparison reference and [29 ,reference30] review, [29,30] the shear review, stress the transport shear stress (SST) transportk ω turbulent (SST) k modelturbulent and the model scalable and − wallthe functionscalable arewall adopted. function Because are adopted. the flow Because collection the flow and distributioncollection and are distribution difficult to simulate are difficult in the to 2Dsimulate model, thein the fluid 2D fields model, in di thefferent fluid parts fields are in assumed different independent parts are assumed with given independent boundaries conditionswith given asboundaries listed in Table conditions3. as listed in Table 3.

TableTable 3. 3.Boundaries Boundaries conditions conditions adopted adopted in in the the thermal-hydraulics thermal-hydraulics calculation. calculation.

PartsParts InletInlet Temperature Temperature (◦ C)(°C) Average Average Velocity (m(m/s)/s) Pressure Pressure Drop Drop (kPa) (kPa) FW 300 18.3 7.5 FW 300 18.3 7.5 CP1CP1 435435 44.1 86.4 86.4 CP2CP2 435435 44.5 87.0 87.0 CP3CP3 435435 43.8 87.3 87.3 CP4CP4 435435 43.1 86.4 86.4 CP5CP5 435435 43.8 87.6 87.6 CP6CP6 435435 43.9 88.5 88.5

Figure 9 shows the 2D thermal-hydraulics model of the HCSB blanket and the helium flow Figure9 shows the 2D thermal-hydraulics model of the HCSB blanket and the helium flow directions. To ensure that the simulation results are independent of the grid. The grid independent directions. To ensure that the simulation results are independent of the grid. The grid independent analysis is carried out based on the one-way N/TH coupling calculation. The most concerned analysis is carried out based on the one-way N/TH coupling calculation. The most concerned variables variables in the N/TH coupling calculation include the coolant density and the material temperature. in the N/TH coupling calculation include the coolant density and the material temperature. Therefore, Therefore, the coolant densities at the outlets and the maximum temperature are selected to analyze. the coolant densities at the outlets and the maximum temperature are selected to analyze. Three sets Three sets of grids, Grid #1, Grid #2, and Grid #3, are investigated, the element counts of which are of grids, Grid #1, Grid #2, and Grid #3, are investigated, the element counts of which are 161,194, 161,194, 477,527, and 954,127, respectively. Table 4 shows the results. It can be seen that the Grid #2 477,527, and 954,127, respectively. Table4 shows the results. It can be seen that the Grid #2 gives a grid gives a grid independent result and the Grid #2 is chosen to perform the N/TH coupling calculation. independent result and the Grid #2 is chosen to perform the N/TH coupling calculation.

FigureFigure 9. 9.The The 2D 2D HSCB HSCB thermal-hydraulics thermal-hydraulics model. model.

Table 4. Thermal-hydraulics results comparison of the HCSB with different grids.

Variations Grid #1 Grid #2 Grid #3 Element counts 161,194 477,527 954,127 Coolant density at FW outlet (kg/m3) 6.299106 6.295557 6.295696 Coolant density at CP1 outlet (kg/m3) 5.339649 5.338095 5.338031 Coolant density at CP2 outlet (kg/m3) 5.182181 5.181435 5.181607 Coolant density at CP3 outlet (kg/m3) 5.217227 5.216613 5.216785 Coolant density at CP4 outlet (kg/m3) 5.327579 5.327155 5.325293 Coolant density at CP5 outlet (kg/m3) 5.426092 5.425874 5.425687 Coolant density at CP6 outlet (kg/m3) 5.463196 5.463004 5.463052 Maximum temperature (◦C) 859.3649 859.1595 859.1474 Energies 2020, 13, x FOR PEER REVIEW 9 of 22

Table 4. Thermal-hydraulics results comparison of the HCSB with different grids.

Variations Grid #1 Grid #2 Grid #3 Element counts 161,194 477,527 954,127 Coolant density at FW outlet (kg/m3) 6.299106 6.295557 6.295696 Coolant density at CP1 outlet (kg/m3) 5.339649 5.338095 5.338031 Coolant density at CP2 outlet (kg/m3) 5.182181 5.181435 5.181607 Coolant density at CP3 outlet (kg/m3) 5.217227 5.216613 5.216785 Coolant density at CP4 outlet (kg/m3) 5.327579 5.327155 5.325293 Coolant density at CP5 outlet (kg/m3) 5.426092 5.425874 5.425687 Coolant density at CP6 outlet (kg/m3) 5.463196 5.463004 5.463052 Energies 2020, 13, 4070 9 of 20 Maximum temperature (°C) 859.3649 859.1595 859.1474

2.3.2.3. WCCB WCCB Blanket Blanket Model Model TheThe conceptual conceptual design design of of the the WCCB WCCB [31] [31 ]blanket blanket for for the the CFETR, CFETR, based based on on the the mature mature pressurized pressurized waterwater reactor reactor technology, technology, was was proposed proposed by by the the In Institutestitute of of Plasma Plasma Phys Physicsics Chinese Chinese Academy Academy of of SciencesSciences (ASIPP). (ASIPP). Figure Figure 1010 showsshows the the typical typical st structureructure design design of of the the W WCCBCCB blanket. The The WCCB WCCB blanketblanket is is mainly mainly composed of FW, mixingmixing pebblepebble beds, beds, CPs, CPs, SPs, SPs, side side walls walls (SWs), (SWs), manifolds, manifolds, and and BP. BP.The The overall overall dimensions dimensions are 1199 are mm1199 (poloidal), mm (poloidal), 802 mm 802 (radial), mm and(radial), 950 mm and (toroidal), 950 mm respectively.(toroidal), respectively.The FW is a The U-shape FW is structure a U-shape along structure the radial-poloidal-radial along the radial-poloidal-radial directions. Adirections. layer with A alayer thickness with aof thickness 2 mm of of tungsten 2 mm of armor tungsten covers armor on the covers FW toon protect the FW the to FWprotect from the plasma FW from corrosion plasma and corrosion erosion. andForty-two erosion. channels Forty-two with channels the cross with section the cross of 8section mm of8 8 mm mm are× 8 arrangedmm are arranged in parallel in parallel with the with FW. the FW. To maintain chemistry stability, the WCCB ×adopts the mixing pebble beds consisting of To maintain chemistry stability, the WCCB adopts the mixing pebble beds consisting of Li2TiO3 Li2TiO3 and Be12Ti as the breeding material. Two layers of beryllium pebble beds are inserted to the and Be12Ti as the breeding material. Two layers of beryllium pebble beds are inserted to the BZ to BZenhance to enhance the neutron-multiplying the neutron-multiplying capability. capability Light-water. Light-water with a pressure with a pressure of 15.5 MPa of and15.5 inletMPa/outlet and inlet/outlet temperature of 285 °C and 325 °C is employed as the coolant. Main design parameters temperature of 285 ◦C and 325 ◦C is employed as the coolant. Main design parameters and material andcompositions material compositions of the WCCB of blanket the WCCB #3 are blan listedket in#3 Tablesare listed5 and in6 Table. 5 and Table 6.

Energies 2020, 13, x FOR PEER REVIEW 10 of 22

(a) (b)

(c) (d)

Figure 10. The structure of the typical Water-Cooled Ceramic Breeder (WCCB) blanket: Figure(a) Explosive 10. The view structure of the of WCCB the typical blanket; Water-Cooled (b) Partially Ceramic enlarged Breeder schematic; (WCCB) (c) Toroidalblanket: ( cross-section;a) Explosive view(d) Poloidal of the WCCB cross-section. blanket; (b) Partially enlarged schematic; (c) Toroidal cross-section; (d) Poloidal cross-section. According to literature [9], Figures 11 and 12 show the 3D neutronics model and the NWL 2 distribution of the blankets,Table 5. Main respectively. parts dimensions The blanket of the #3, WCCB whose blanket NWL #3 is module. 0.454 MW /m , is selected to perform the N/TH coupling analysis. Similar to the HCSB, the WCCB blanket model is simplified to a 1D cylinderItems neutronics model and a 2D thermal-hydraulics Parameters model for the N/TH coupling calculation. Blanket size Poloidal height: 1199 mm; toroidal width: 950 mm; radial thickness: 802 mm Figure 13 shows the radial layout of the 1D WCCB neutronics model. Tungsten armor 2 mm FW Thickness: 20 mm; channel: U-shaped, cross section 8 mm × 8 mm, pitch 22 mm Radial thickness: 53/30/77/30/139/327 mm BU CPs: thickness: 11 mm, Channels: cross section 5 mm × 5 mm, pitch 15 mm

Table 6. Material selections of the WCCB blanket.

Items Material Components Structural materials RAFM steel Breeder 14.4% Li2TiO3, 65.6% Be12Ti, 20% Helium Neutron multiplier 80% Beryllium, 20% helium Back plate 20% light water, 80% RAFM steel Coolant 100% light water of 15.5 MPa

According to literature [9], Figure 11 and Figure 12 show the 3D neutronics model and the NWL distribution of the blankets, respectively. The blanket #3, whose NWL is 0.454 MW/m2, is selected to perform the N/TH coupling analysis. Similar to the HCSB, the WCCB blanket model is simplified to a 1D cylinder neutronics model and a 2D thermal-hydraulics model for the N/TH coupling calculation. Figure 13 shows the radial layout of the 1D WCCB neutronics model.

Energies 2020, 13, 4070 10 of 20

Table 5. Main parts dimensions of the WCCB blanket #3 module.

Items Parameters Blanket size Poloidal height: 1199 mm; toroidal width: 950 mm; radial thickness: 802 mm Tungsten armor 2 mm FW Thickness: 20 mm; channel: U-shaped, cross section 8 mm 8 mm, pitch 22 mm × Radial thickness: 53/30/77/30/139/327 mm BU CPs: thickness: 11 mm, Channels: cross section 5 mm 5 mm, pitch 15 mm ×

Table 6. Material selections of the WCCB blanket.

Items Material Components Structural materials RAFM steel Breeder 14.4% Li2TiO3, 65.6% Be12Ti, 20% Helium Neutron multiplier 80% Beryllium, 20% helium Energies 2020, 13, x FOR PEER REVIEW 11 of 22 Back plate 20% light water, 80% RAFM steel Energies 2020, 13, x FOR PEER REVIEWCoolant 100% light water of 15.5 MPa 11 of 22

Figure 11. Vertical cross section of the CFETR with the WCCB neutronics model. Figure 11. Vertical cross section of the CFETR with the WCCB neutronics model. Figure 11. Vertical cross section of the CFETR with the WCCB neutronics model.

Figure 12. NWL on each WCCB blanket module. Figure 12. NWL on each WCCB blanket module.

Figure 12. NWL on each WCCB blanket module.

Figure 13. Radial layout of the 1D WCCB neutronics model.

Figure 13. Radial layout of the 1D WCCB neutronics model.

Energies 2020, 13, x FOR PEER REVIEW 11 of 22

Figure 11. Vertical cross section of the CFETR with the WCCB neutronics model.

Energies 2020, 13, 4070 Figure 12. NWL on each WCCB blanket module. 11 of 20

Energies 2020, 13, x FOR PEERFigure REVIEW 13. Radial layout of the 1D WCCB neutronics model. 12 of 22 Figure 13. Radial layout of the 1D WCCB neutronics model.

FigureFigure 1010b,db,d showshow thethe flowflow schemescheme ofof thethe waterwater coolant. coolant. ChannelsChannels betweenbetween adjacentadjacent CPsCPs areare connectedconnected one one by by one. one. The The water water coolant, coolant, with with the the temperature temperature to to be be 285 285◦C °C and and with with the the pressure pressure to be to

15.5be 15.5 MPa, MPa, comes comes from from the blanket the blanket inlet. Firstly,inlet. Firstly, the water the coolant water flowscoolant into flows the FW.into Then, the FW. the waterThen, outthe ofwater the FWout channelsof the FW goes channels through goes the through CP #1 to the the CP CP #1 #4 to in the turn. CP The#4 in simplified turn. The 2Dsimplified thermal-hydraulics 2D thermal- modelhydraulics is shown model in is Figure shown 14 .in Figure 14.

Figure 14. The 2D WCCB thermal-hydraulics model. Figure 14. The 2D WCCB thermal-hydraulics model. In the thermal-hydraulics calculation, the heat flux to the FW is 0.3 MW/m2. To achieve an outlet In the thermal-hydraulics calculation, the heat flux to the FW is 0.3 MW/m2. To achieve an outlet temperature as the designed parameter, the mass flow rate is determined according to the total nuclear temperature as the designed parameter, the mass flow rate is determined according to the total power deposition obtained from the one-way coupling calculation. In the thermal-hydraulics model, nuclear power deposition obtained from the one-way coupling calculation. In the thermal-hydraulics elbow pipes are assigned to connect channels for coolant transfer. The SST k ω turbulent model is model, elbow pipes are assigned to connect channels for coolant transfer. The− SST k −ω turbulent employed to deal with the phenomenon of boundary layer separation according to the recommendation model is employed to deal with the phenomenon of boundary layer separation according to the of reference [32] at elbows. The results of the grid independent analysis are shown in Table7. It can be recommendation of reference [32] at elbows. The results of the grid independent analysis are shown seen that the differences are very small among the different grids. To save computational resources, in Table 7. It can be seen that the differences are very small among the different grids. To save the Grid #2 is chosen to perform the N/TH coupling calculation. computational resources, the Grid #2 is chosen to perform the N/TH coupling calculation. Table 7. Thermal-hydraulics results comparison of the WCCB with different grids. Table 7. Thermal-hydraulics results comparison of the WCCB with different grids. Variations Grid #1 Grid #2 Grid #3 Variations Grid #1 Grid #2 Grid #3 ElementElement counts counts 106,180 106,180 687,436 687,436 1,661,151 1,661,151 3 CoolantCoolant density density at outlet at (kgoutlet/m (kg/m) 3687.5223) 687.5223 687.4366 687.4366 687.7029 687.7029 Maximum temperature ( C) 965.0614 964.6455 965.3698 Maximum temperature◦ (℃) 965.0614 964.6455 965.3698

3. Results

3.1. The N/TH Coupling Calculation of HCSB Blanket

3.1.1. The Sensitivity Analyses of Temperature Before performing the two-way N/TH coupling calculation, the sensitivity analyses of the material temperature of the neutron multiplier and the tritium breeder are carried out. It is helpful to understand how temperature affects the neutronics performance and explains the coupling results in the later section. In particular, it should be noted that the cross sections data from S (α, β) tables which give a complete representation of thermal neutron elastic and inelastic scattering by molecules and crystalline solids in the neutron energies range below than 4 eV are not provided in the FENDL-2.1 library. Neutronic calculation without the S (α, β) will lead to an inaccurate TBR, because the thermal neutron has a considerable contribution to the TBR. Hence, the S (α, β) data from ENDF/B-VII.0 are used in this calculation

Energies 2020, 13, 4070 12 of 20

3. Results

3.1. The N/TH Coupling Calculation of HCSB Blanket

3.1.1. The Sensitivity Analyses of Temperature Before performing the two-way N/TH coupling calculation, the sensitivity analyses of the material temperature of the neutron multiplier and the tritium breeder are carried out. It is helpful to understand how temperature affects the neutronics performance and explains the coupling results in the later section. In particular, it should be noted that the cross sections data from S (α, β) tables which give a complete representation of thermal neutron elastic and inelastic scattering by molecules and crystalline solids in the neutron energies range below than 4 eV are not provided in the FENDL-2.1 library. Neutronic calculation without the S (α, β) will lead to an inaccurate TBR, because the thermal neutron has a considerable contribution to the TBR. Hence, the S (α, β) data from ENDF/B-VII.0 are used in this calculation. Table8 presents the calculation results without considering the S (α, β) data, and Table9 presents the calculation results with considering the S (α, β) data. The situations of neutron multiplier and the tritium breeder at 20 ◦C, 327 ◦C, 627 ◦C, and 927 ◦C are calculated. The TBR and nuclear heat deposition are normalized to one source neutron.

Table 8. Neutronics results of the HCSB blanket without considering the S (α, β) data at different materials temperatures.

Items 20 ◦C 327 ◦C 627 ◦C 927 ◦C TBR at different beryllium temperature 1.575489 1.574678 1.575460 1.576541 TBR at different Li4SiO4 temperature 1.576954 1.576950 1.576945 Total nuclear heat deposition at different 18.964842 18.972012 18.964625 beryllium temperature (eV) 18.988849 Total nuclear heat deposition at different Li4SiO4 18.972121 18.961930 18.971926 temperature (eV)

Table 9. Neutronics results of the HCSB blanket with considering the S (α, β) data at different materials temperatures.

Items 20 ◦C 327 ◦C 627 ◦C 927 ◦C TBR at different beryllium temperature 1.590735 1.596369 1.602417 1.577718 TBR at different Li4SiO4 temperature 1.578197 1.578201 1.578195 Total nuclear heat deposition of different 18.933757 18.913840 18.908857 beryllium temperature (eV) 18.963606 Total nuclear heat deposition of different Li SiO 4 4 18.968743 18.968764 18.968599 temperature (eV)

From the comparison between the results at 20 ◦C in Tables8 and9, it can be observed that the TBR is larger and the nuclear heat deposition is smaller with considering the thermal scattering treatment. When the S (α, β) data are not taken into account, there are only very small differences among the results at different temperatures, which is contrary to the reality. Thus, the S (α, β) data will make calculation results different, and should be considered in the N/TH coupling calculation. From Table9, the results reveal that the TBR is increasing as the beryllium temperature rises. Reason of this tendency is that, as the beryllium temperature increases, the neutron thermal scattering cross section increases, leading to more thermal neutrons. The total nuclear heat deposition decreases with the increasing of the temperature of the beryllium, and the changing rate decreases gradually. The reason is that the increases of the heat deposition in the breeder zones are less than the decreases of Energies 2020, 13, 4070 13 of 20

the heat deposition in the neutron multiplier zones. As for the temperature effects of Li4SiO4, TBR and nuclear heat deposition have a temporary rise between 20 ◦C and 327 ◦C, then remain stable. To sum up, TBR and nuclear heat deposition of the HCSB blanket will increase as temperature rises.

3.1.2. The N/TH Coupling Results The coupling calculation begins with the neutronics calculation with a uniform temperature distribution of 20 ◦C. Table 10 lists the TBR, relative percentage standard deviation of TBR, and associated differences during the iteration process. The one-way N/TH coupling calculation is equal to the Iteration #0 in the two-way N/TH coupling calculation. The Iteration #2 is convergent. The TBR obtained from the two-way N/TH coupling calculation is 0.11% smaller than the one-way N/TH coupling calculation. As helium is transparent to neutron, the change of helium density will not impact neutronics results. Combined with the sensitivity analyses of the materials temperature, the two-way N/TH coupling effect should be mainly dominantly caused by the thermal scattering effect of the beryllium in the HCSB blanket. However, the more neutrons are absorbed by the steel at high temperature because of the Doppler-effect. As a result, the two-way N/TH coupling effect causes a small influence on TBR.

Table 10. TBR variation in the two-way N/TH coupling calculation of the HCSB blanket.

Iteration #1 Iteration #2 Items Iteration #0 (Value and Relative Difference) (Value & Relative Difference) 0.767531 0.05% 0.767529 0.05% Local TBR in BZ1 0.771213 0.05% ± ± ± ( 0.4774%) ( 0.0002%) − − 0.648876 0.06% 0.648872 0.06% Local TBR in BZ2 0.648153 0.06% ± ± ± (0.1115%) ( 0.0006%) − 0.159586 0.13% 0.159586 0.13% Local TBR in BZ3 0.158352 0.13% ± ± ± (0.7791%) (0.0001%) 1.575993 0.06% 1.575987 0.06% Total TBR 1.577718 0.06% ± ± ± ( 0.1094%) ( 0.0004%) − −

As shown in Figure 15, the power density decreases along the radial direction in the zones with the same material. The nuclear heat power density of the tungsten armor is the maximum, because the high-energy neutron stream from the plasma directly penetrates the tungsten armor. Besides, the power densities are relatively high in BZs, and low in MZs. This is mainly determined by the high heat release cross sections of the tritium breeder. Figure 16 shows the relative differences of the power density between the two-way and one-way N/TH coupling calculations (one-way results are used as the reference values). There are very small differences between the one-way and two-way coupling calculations. Compared with the power densities obtained from the one-way N/TH coupling calculation, the power densities obtained from the two-way N/TH coupling calculation are overestimated in armor, MZ1 and BZ1, and underestimated in other zones. The power density in CPs increases, because the more neutrons are absorbed by the structural material at high temperature. Figure 17 shows the temperature distribution contour of the HCSB blanket obtained from the one-way coupling and two-way coupling calculations. Figure 18 shows the radial temperature distribution curve in the middle position of the poloidal direction of HCSB blanket obtained from the one-way and two-way coupling calculations, respectively. Obviously, the temperature changes greatly along the radial direction and changes slightly along the poloidal direction. Most nuclear heat is deposited in BZs due to the high power density and the high volume ratio. CPs are inserted into the interfaces between the BZ and the MZ. Therefore, the temperature curves in BZs and MZs show the cosine shape with the local maximum temperature appearing at the center. Because of the high nuclear heat deposition and the poor heat conductive capability of the tritium breeder, the global maximum temperature appears at the second BZ. Although there are a high heat flux and a high nuclear heat deposit in the tungsten armor and FW, the ample cooling capability ensures that the heat deposition in them could be removed so that the temperatures are kept at a low level. Energies 2020, 13, x FOR PEER REVIEW 14 of 22

Table 10. TBR variation in the two-way N/TH coupling calculation of the HCSB blanket.

Iteration #1 Iteration #2 Items Iteration #0 (Value and Relative Difference) (Value & Relative Difference) 0.767531 ± 0.05% 0.767529 ± 0.05% Local TBR in BZ1 0.771213 ± 0.05% (−0.4774%) (−0.0002%) 0.648876 ± 0.06% 0.648872 ± 0.06% Local TBR in BZ2 0.648153 ± 0.06% (0.1115%) (−0.0006%) 0.159586 ± 0.13% 0.159586 ± 0.13% Local TBR in BZ3 0.158352 ± 0.13% (0.7791%) (0.0001%) 1.575993 ± 0.06% 1.575987 ± 0.06% Total TBR 1.577718 ± 0.06% (−0.1094%) (−0.0004%)

As shown in Figure 15, the power density decreases along the radial direction in the zones with the same material. The nuclear heat power density of the tungsten armor is the maximum, because the high-energy neutron stream from the plasma directly penetrates the tungsten armor. Besides, the power densities are relatively high in BZs, and low in MZs. This is mainly determined by the high heat release cross sections of the tritium breeder. Figure 16 shows the relative differences of the power density between the two-way and one-way N/TH coupling calculations (one-way results are used as the reference values). There are very small differences between the one-way and two-way coupling calculations. Compared with the power densities obtained from the one-way N/TH coupling calculation, the power densities obtained from the two-way N/TH coupling calculation are overestimated in armor, MZ1 and BZ1, and underestimated in other zones. The power density in CPs Energies 2020, 13, 4070 14 of 20 increases, because the more neutrons are absorbed by the structural material at high temperature.

Energies 2020, 13, x FOR PEER REVIEW 15 of 22 Figure 15. Radial power density distribution of the HCSB blanket. Figure 15. Radial power density distribution of the HCSB blanket.

Figure 16. The relative differences of the power density between the one-way and two-way N/TH Figure 16. The relative differences of the power density between the one-way and two-way N/TH couplingEnergies 2020 calculations., 13, x FOR PEER REVIEW 16 of 22 coupling calculations.

Figure 17 shows the temperature distribution contour of the HCSB blanket obtained from the one-way coupling and two-way coupling calculations. Figure 18 shows the radial temperature distribution curve in the middle position of the poloidal direction of HCSB blanket obtained from the one-way and two-way coupling calculations, respectively. Obviously, the temperature changes greatly along the radial direction and changes slightly along the poloidal direction. Most nuclear heat is deposited in BZs due to the high power density and the high volume ratio. CPs are inserted into the interfaces between the BZ and the MZ. Therefore, the temperature curves in BZs and MZs show the cosine shape with the local maximum temperature appearing at the center. Because of the high nuclear heat deposition and the poor heat conductive capability of the tritium breeder, the global maximum temperature appears at the second BZ. Although there are a high heat flux and a high nuclear heat deposit in the tungsten armor and FW, the ample cooling capability ensures that the heat deposition in them could be removed so that the temperatures are kept at a low level. Compared with the one-way(a) N/TH coupling calculation, the temperature(b) distribution obtained from the two-way coupling N/TH calculation increases in BZs and decreases in MZs. The nuclear FigureFigure 17. Temperature 17. Temperature distribution distribution in in thethe HCSB HCSB blanket: blanket: (a) (one-waya) one-way N/TH N coupling/TH coupling calculation; calculation; (b) heat deposition changes slightly. The temperature differences between the one-way and two-way (b) two-waytwo-way N N/TH/TH coupling coupling calculation. N/TH coupling calculations are small, because the differences of the power density are small in most zones. The relative power density changes in CPs are positive. As the thermal conductivity of CP is high and the heat power density changes are small, the temperature changes of the CPs are small. The maximum temperature difference appears at the fourth BZ, which is about 1 °C. It is concluded that the two-way N/TH coupling effect has a very small effect on the temperature distribution in the HCSB blanket.

Figure 18. Comparison of the temperature distribution along the radial direction.

3.2. The N/TH Coupling Calculation of WCCB Blanket

3.2.1. The Sensitivity Analyses of Temperature Different from helium, light-water, which possesses the excellent neutron-moderating capability, will affect the neutron spectrum and generate more thermal neutrons in blanket. Considering the tritium production cross sections of the lithium are large in the low-energy ranges, the changes of density and temperature of water will obviously influence the TBR. To investigate and understand the temperature effect in different materials in the WCCB, the temperature sensitivity analyses of tritium breeder, neutron multiplier, and coolant are carried out. The temperatures of all materials are set to 20 °C firstly, and the density of water depends on its temperature. Because the saturated temperature of water is 345 °C with the pressure to be 15.5 MPa, only cases with 20 °C and 327 °C are calculated. The importance of the S (α, β) table was proven in the previous section, so the cases without considering S (α, β) are not calculated in this section. Table 11 lists the calculation results. The variation tendencies of the neutron multiplier and the tritium breeder are similar to the HCSB. When the neutron multiplier temperature increases, the TBR increases, but the nuclear heat deposition decreases. Because the volume fraction of the neutron multiplier is small in the WCCB, the temperature effect has been diminished. Between 20 °C and 327 °C, the TBR and the nuclear heat deposition increase with the increase of the tritium breeder

Energies 2020, 13, x FOR PEER REVIEW 16 of 22

(a) (b)

Figure 17. Temperature distribution in the HCSB blanket: (a) one-way N/TH coupling calculation; (b) Energies 2020, 13, 4070 15 of 20 two-way N/TH coupling calculation.

FigureFigure 18.18. Comparison ofof thethe temperaturetemperature distributiondistribution alongalong thethe radialradial direction.direction.

3.2. TheCompared N/TH Coupling with the Calc one-wayulation Nof/ THWCCB coupling Blanket calculation, the temperature distribution obtained from the two-way coupling N/TH calculation increases in BZs and decreases in MZs. The nuclear heat deposition3.2.1. The Sensitivity changes slightly. Analyses The of temperatureTemperature di fferences between the one-way and two-way N/TH coupling calculations are small, because the differences of the power density are small in most zones. TheDifferent relative from power helium, density light-water, changes in CPswhich are positive.possesses As the the excellent thermal conductivityneutron-moderating of CP is highcapability, and the will heat affect power the density neutron changes spectrum are small, and thegenerate temperature more thermal changes neutrons of the CPs in are blanket. small. Considering the tritium production cross sections of the lithium are large in the low-energy ranges, The maximum temperature difference appears at the fourth BZ, which is about 1 ◦C. It is concluded thatthe changes the two-way of density N/TH and coupling temperature effecthas of water a very will small obviously effect on influence the temperature the TBR. distributionTo investigate in and the HCSBunderstand blanket. the temperature effect in different materials in the WCCB, the temperature sensitivity analyses of tritium breeder, neutron multiplier, and coolant are carried out. The temperatures of all 3.2.materials The N /THare Couplingset to 20 Calculation°C firstly, and of WCCB the density Blanket of water depends on its temperature. Because the saturated temperature of water is 345 °C with the pressure to be 15.5 MPa, only cases with 20 °C and 3.2.1.327 °C The are Sensitivity calculated. Analyses The importance of Temperature of the S (α, β) table was proven in the previous section, so the casesDi withoutfferent fromconsidering helium, S light-water, (α, β) are not which calculated possesses in this the excellentsection. neutron-moderating capability, will aTableffect the11 lists neutron the calculation spectrum andresults. generate The variation more thermal tendencies neutrons of the in neutron blanket. multiplier Considering and thethe tritiumtritium productionbreeder are similar cross sections to the HCSB. of the When lithium the are neutron large inmultiplier the low-energy temperature ranges, increases, the changes the TBR of densityincreases, and but temperature the nuclear of heat water deposition will obviously decreas influencees. Because the TBR.the volume To investigate fraction and of understandthe neutron themultiplier temperature is small eff inect the in WCCB, different the materials temperature in the effect WCCB, has been the temperature diminished. sensitivityBetween 20 analyses °C and 327 of tritium°C, the breeder,TBR and neutron the nuclear multiplier, heat anddeposition coolant increase are carried with out. the The increase temperatures of the tritium of all materials breeder are set to 20 ◦C firstly, and the density of water depends on its temperature. Because the saturated temperature of water is 345 ◦C with the pressure to be 15.5 MPa, only cases with 20 ◦C and 327 ◦C are calculated. The importance of the S (α, β) table was proven in the previous section, so the cases without considering S (α, β) are not calculated in this section. Table 11 lists the calculation results. The variation tendencies of the neutron multiplier and the tritium breeder are similar to the HCSB. When the neutron multiplier temperature increases, the TBR increases, but the nuclear heat deposition decreases. Because the volume fraction of the neutron multiplier is small in the WCCB, the temperature effect has been diminished. Between 20 ◦C and 327 ◦C, the TBR and the nuclear heat deposition increase with the increase of the tritium breeder temperature. When the temperature of the tritium breeder is between 327 ◦C and 927 ◦C, the TBR and nuclear heat deposition remain stable. Energies 2020, 13, 4070 16 of 20

Table 11. Neutronics results of the WCCB blanket at different materials temperatures.

Items 20 ◦C 327 ◦C 627 ◦C 927 ◦C TBR at different beryllium temperature 1.451849 1.452164 1.445660 TBR at different breeder temperature1.451630 1.457769 1.457794 1.457555 TBR at different coolant temperature 1.531576 // Total nuclear heat deposition at different 19.450326 19.449406 19.400373 beryllium temperature (eV) Total nuclear heat deposition at different 19.453868 19.481066 19.481712 19.481288 breeder temperature (eV) Total nuclear heat deposition at different 19.466556 // coolant temperature (eV)

There is a noticeable increase in the TBR when the coolant temperature increases from 20 ◦C to 3 3 327 ◦C. The primary reason is that the density of water drops from 1.0 g/cm to 0.6 g/cm . Although the neutron-moderating capability of water is weaker because of the low coolant density, more neutrons escape from the absorption of the coolant, and react with the breeder. Therefore, decreasing water density could effectively enhance the TBR.

3.2.2. The N/TH Coupling Results The coupling calculation begins with the neutronics calculation with a uniform temperature of 20 ◦C. Table 12 lists the TBR and associated differences during the WCCB coupling iteration process. Iteration #0 means the one-way N/TH coupling calculation. After one iteration, the two-way N/TH coupling calculation is converged. Compared with the one-way coupling calculation, the coolant density is smaller, and the breeder temperature is higher in the two-way coupling calculation, hence the TBR increases by 4.45%. The influence of coolant temperature is significant. Moreover, there are more obvious impacts on the BZ, which is further away from the tungsten armor. It reveals that the two-way N/TH coupling effect has a significant impact in the WCCB blanket.

Table 12. TBR variation in the two-way N/TH coupling calculation of the WCCB blanket.

Iteration #0 Iteration #1 Iteration #2 Items (Value) (Value and Relative Difference) (Value and Relative Difference) 0.597635 0.06% 0.597600 0.06% Local TBR in BZ1 0.587849 0.06% ± ± ± (1.6647%) ( 0.0006%) − 0.539266 0.07% 0.538988 0.07% Local TBR in BZ2 0.515862 0.07% ± ± ± (4.5369%) ( 0.0516%) − 0.294728 0.10% 0.293750 0.10% Local TBR in BZ3 0.270865 0.10% ± ± ± (8.8099%) ( 0.3318%) − 0.086122 0.19% 0.085868 0.19% Local TBR in BZ4 0.077054 0.20% ± ± ± (11.7684%) ( 0.2949%) − 1.517741 0.08% 1.516206 0.08% Total TBR 1.451630 0.08% ± ± ± (4.5355%) ( 0.1011%) −

As shown in Figure 19, the power density decreases along the radial direction in the zones with the same materials. The maximum nuclear heat power density appears at the tungsten armor. The power densities in the BZs are higher than the adjacent MZs. Figure 20 shows the relative differences of the power density distribution between the one-way and two-way N/TH coupling calculations. The power densities increase in BZs and MZs, and the relative differences increase more in the BZs, which are further away from the tungsten armor. It will lead to the temperature increase in the BZs and influence the safety of the blanket. The power density decreases in other zones. In the FW and CPs, there are great decreases in the relative power density differences between the one-way and two-way N/TH coupling calculations. This is mainly caused by the following two reasons: (1) when the coolant density decreases, the nuclear heat deposition in water decreases; (2) with the weaker neutron-moderating Energies 2020, 13, x FOR PEER REVIEW 18 of 22

Energies 2020, 13, x FOR PEER REVIEW 18 of 22 CPs, there are great decreases in the relative power density differences between the one-way and two-way N/TH coupling calculations. This is mainly caused by the following two reasons: (1) when CPs, there are great decreases in the relative power density differences between the one-way and Energiesthe coolant2020, 13 density, 4070 decreases, the nuclear heat deposition in water decreases; (2) with the weaker17 of 20 two-way N/TH coupling calculations. This is mainly caused by the following two reasons: (1) when neutron-moderating capability of the low-density water, fewer thermal neutrons are produced and the coolant density decreases, the nuclear heat deposition in water decreases; (2) with the weaker absorbed by the steel. Therefore, the nuclear heat produced by steel decreases. capabilityneutron-moderating of the low-density capability water, of the fewer low-density thermal neutronswater, fewer are producedthermal neutrons and absorbed are produced by the steel. and Therefore,absorbed by the the nuclear steel. heatTherefore, produced the nu byclear steel heat decreases. produced by steel decreases.

Figure 19. Radial power density distribution of the WCCB blanket. FigureFigure 19.19. Radial power densitydensity distributiondistribution ofof thethe WCCBWCCB blanket.blanket.

Figure 20. The relative differences of power density between the one-way and two-way N/TH couplingFigure 20. calculations. The relative differences of power density between the one-way and two-way N/TH coupling calculations. Figure 20. The relative differences of power density between the one-way and two-way N/TH Figure 21 shows the temperature distribution contour of the WCCB blanket obtained from the coupling calculations. one-wayFigure and 21 two-way shows Nthe/TH temperature coupling calculations. distribution Figure contour 22 shows of the theWCCB radial blanket temperature obtained distribution from the curveone-way at the and middle two-way position N/TH of the coupling poloidal direction.calculatio Thens. temperatureFigure 22 distributionsshows the radial of two temperature calculations Figure 21 shows the temperature distribution contour of the WCCB blanket obtained from the aredistribution similar: temperature curve at the changes middle greatly position along of the the po radialloidal direction, direction. and The the temperature local maximum distributions temperature of one-way and two-way N/TH coupling calculations. Figure 22 shows the radial temperature appearstwo calculations at the center are ofsimilar: BZs.In temperature the one-way changes N/TH couplinggreatly along calculation, the radial the maximumdirection, and temperature the local distribution curve at the middle position of the poloidal direction. The temperature distributions of ismaximum 960 C, and temperature appears at appears the center at the of center the first of BZBZs. because In the one-way of the maximum N/TH coupling power density.calculation, Inthe the two calculations◦ are similar: temperature changes greatly along the radial direction, and the local two-waymaximum N /temperatureTH coupling calculation,is 960 °C, and the appears maximum at the temperature center of appearingthe first BZ at because the central of the of the maximum first BZ maximum temperature appears at the center of BZs. In the one-way N/TH coupling calculation, the ispower 973 C.density. Compared In the with two-way the one-way N/TH coupling N/TH coupling calculation, calculation, the maximum in the two-waytemperature N/TH appearing coupling at maximum◦ temperature is 960 °C, and appears at the center of the first BZ because of the maximum calculation,the central of the the maximum first BZ is temperature 973 °C. Compared increases with in the four one-way BZs are N/TH 13 C, coupling 22 C, 29calculation,C, and 26 in theC, power density. In the two-way N/TH coupling calculation, the maximum◦ temperature◦ ◦ appearing◦ at respectively. The ignorance of the two-way N/TH coupling effect may lead the temperature to exceed the central of the first BZ is 973 °C. Compared with the one-way N/TH coupling calculation, in the the temperature limit in the actual operation of CFETR. From the perspective of reactor safety, it is necessary to consider the two-way N/TH coupling effect in the blanket design. Energies 2020, 13, x FOR PEER REVIEW 19 of 22 Energies 2020, 13, x FOR PEER REVIEW 19 of 22 two-way N/TH coupling calculation, the maximum temperature increases in four BZs are 13 °C, 22 two-way N/TH coupling calculation, the maximum temperature increases in four BZs are 13 °C, 22 °C, 29 °C, and 26 °C, respectively. The ignorance of the two-way N/TH coupling effect may lead the °C, 29 °C, and 26 °C, respectively. The ignorance of the two-way N/TH coupling effect may lead the temperature to exceed the temperature limit in the actual operation of CFETR. From the perspective temperature to exceed the temperature limit in the actual operation of CFETR. From the perspective Energiesof reactor2020, safety,13, 4070 it is necessary to consider the two-way N/TH coupling effect in the blanket design.18 of 20 of reactor safety, it is necessary to consider the two-way N/TH coupling effect in the blanket design.

(a) (b) (a) (b) Figure 21. Temperature distribution in the WCCB blanket: (a) one-way N/TH coupling calculation; FigureFigure 21. 21.Temperature Temperature distribution distribution in in the the WCCB WCCB blanket: blanket: ( a()a one-way) one-way N N/TH/TH coupling coupling calculation; calculation; (b) two-way N/TH coupling calculation. (b()b two-way) two-way N N/TH/TH coupling coupling calculation. calculation.

FigureFigure 22.22.Comparison Comparison ofof thethe temperaturetemperature distributiondistribution alongalong thethe radial radial direction. direction. Figure 22. Comparison of the temperature distribution along the radial direction. 4. Conclusions 4. Conclusions 4. Conclusions In this paper, the two-way neutronics/thermal-hydraulics (N/TH) coupling effect in neutronics and In this paper, the two-way neutronics/thermal-hydraulics (N/TH) coupling effect in neutronics thermal-hydraulicsIn this paper, calculation the two-way results neutronics/thermal-hydraulics in the China Fusion Engineering (N/TH) Test coupling Reactor effect (CFETR) in neutronics blankets and thermal-hydraulics calculation results in the China Fusion Engineering Test Reactor (CFETR) areand investigated. thermal-hydraulics Firstly, the calculation 3D-1D-2D results hybrid in method the China and Fusion pseudo-material Engineering method Test areReactor proposed (CFETR) to blankets are investigated. Firstly, the 3D-1D-2D hybrid method and pseudo-material method are accelerateblankets theare Ninvestigated./TH coupling Firstly, calculation the 3D-1D-2D based on the hybrid MCNP method and FLUENT. and pseudo-material Moreover, the method sensitivity are proposed to accelerate the N/TH coupling calculation based on the MCNP and FLUENT. Moreover, ofproposed the material to accelerate temperature the N/TH is analyzed coupling to illustrate calculation the based mechanism on the ofMCNP the two-way and FLUENT. coupling Moreover, N TH the sensitivity of the material temperature is analyzed to illustrate the mechanism of the two-way/ the sensitivity of the material temperature is analyzed to illustrate the mechanism of the two-way ecouplingffect. Furthermore, N/TH effect. the Furthermore, one-way and two-waythe one-way N/TH and coupling two-way calculations N/TH coupling are carried calculations out for theare coupling N/TH effect. Furthermore, the one-way and two-way N/TH coupling calculations are helium-cooledcarried out for solidthe helium-cooled breeder (HCSB) solid blanket breeder and (HCS theB) water-cooled blanket and ceramic the water-cooled breeder (WCCB) ceramic blanket. breeder carried out for the helium-cooled solid breeder (HCSB) blanket and the water-cooled ceramic breeder The(WCCB) conclusions blanket. of The the two-wayconclusions N/ THof the coupling two-way eff ectN/TH in the coupling CFETR effect blanket in the are asCFETR follows: blanket are as (WCCB) blanket. The conclusions of the two-way N/TH coupling effect in the CFETR blanket are as follows: 1.follows:Thermal scattering data in the S (α, β) table should be considered in the N/TH coupling calculation 1. ofThermal the CFETR scattering blanket. data in the S (α, β) table should be considered in the N/TH coupling 1. Thermal scattering data in the S (α, β) table should be considered in the N/TH coupling 2. Increasingcalculation the of temperaturethe CFETR blanket. of beryllium could enhance the tritium breeding ratio (TBR), because the calculation of the CFETR blanket. thermal scattering cross sections are large at high temperature.

3. In the HCSB blanket, the two-way N/TH coupling effect will decrease the TBR by 0.11%, and increase the maximum temperature in BZ by 1 ◦C. The N/TH coupling effect could be ignored in the HCSB blanket. Energies 2020, 13, 4070 19 of 20

4. The TBR and nuclear heat deposition are sensitive to the temperature of water, because the density change induced by the temperature change will significantly impact the absorption and moderation capability. 5. In the WCCB blanket, the two-way N/TH coupling effect is more significant. It will enhance the TBR by 4.45%, and increase the maximum temperature of the blanket by 29 ◦C. 6. The relative change of the power density in steel is the largest among all materials in the coupling calculation. However, it will not affect the temperature distribution because the heat deposition could be removed effectively by the neighboring coolant. 7. In general, the CFETR blankets are not so sensitive to the N/TH coupling effect. After only one iteration, the two-way N/TH coupling calculation is convergent. But from the viewpoints of accurate blanket design and safety analysis, it is still valuable to perform the two-way N/TH coupling calculation in fusion water-cooled blankets.

Author Contributions: Conceptualization, T.D.; methodology, T.D.; software, T.D., W.S.; formal analysis, T.D., W.S.; investigation, T.D.; resources, L.C.; data curation, T.D.; writing—original draft preparation, T.D.; writing—review and editing, Q.H., L.C., W.S.; visualization, T.D.; supervision, L.C., H.W.; project administration, L.C.; funding acquisition, L.C., Q.H. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the National Key Research and Development Program of China (No. 2017YFW0302200) and the Young Elite Scientists Sponsorship Program by CAST (No. 2019QNRC001). Acknowledgments: The authors would like to express gratitude to Qixiang Cao, Zaixin Li, Fengchao Zhao, Shen Qu, and Bo Hu from Southwestern Institute of Physics for their valuable guidance in blanket calculation. The authors would also like to express gratitude to reviewers for kindly revising and constructive suggestions. Conflicts of Interest: The authors declare no conflict of interest.

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