Initial optimization of DEMO fusion reactor thermal shields by thermal analysis of its integrated systems

Fusion Engineering and Design 125 (2017) 38–49

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Full Length Article

Initial optimization of DEMO fusion reactor thermal shields by thermal analysis of its integrated systems

T

⁎

Boštjan Končara, , Oriol Costa Garridoa, Martin Drakslera, Richard Brownb, Matti Colemanb,c a b c

Jožef Stefan Institute, Reactor Engineering Division, Jamova cesta 39, SI-1000 Ljubljana, Slovenia PPPT Power Plant Physics and Technology, Eurofusion Consortium, Boltzmannstrasse 2, 85748 Garching, Germany CCFE Fusion Association, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB, United Kingdom

A B S T R A C T Thermal analysis of integrated DEMO cold systems is performed with two main objectives: first to evaluate the static heat loads on the superconducting magnets and thermal shields and second to estimate the optimal working temperature of the thermal shields in order to minimize the total refrigeration power. Thermal radiation and heat conduction loads due to physical connections between the components are considered. Parametric studies are performed to optimize the thermal shields operating temperature based on the theoretical efficiency of the cryogenic cooling system. The effects of vacuum vessel operating temperature and inclusion of passive Multi-Layer Insulation (MLI) on the warm side of the actively cooled thermal shields are analysed. The results suggest that the decrease of vacuum vessel temperature and inclusion of MLI between the vacuum vessel and the thermal shield greatly reduce the theoretical refrigeration power and raise the optimal working temperature of the thermal shields to the values around 100 K.

1. Introduction The ultimate challenge of the international fusion research is exploitation of fusion energy for electricity production contributing to the clean and safe energy mix in the future [1]. The coordinated international research over the past decades resulted in the construction of the largest experimental fusion device ITER that should start its operation in a few years. The next step is to lay down the foundation of a Demonstration Fusion Power Reactor (DEMO) that should be able to produce net electricity in the order of hundreds of MW. Achieving this goal requires establishing a coherent design supported by coordinated research and development activities. DEMO conceptual design activities are carried out within the EUROfusion programme launched in 2014 [2,3]. The DEMO concept pursued within the recent EU fusion roadmap [4] follows a pragmatic approach based on mature technologies, reliable regimes of operation and, to the extent possible, extrapolation from the ITER experience [5]. The current DEMO baseline concept is a tokamak machine designed for long plasma pulses (approximately 2 h). Like ITER, DEMO will rely on superconducting magnets to confine and control the plasma within the vacuum vessel. The superconducting magnets are housed (along with a number of other systems) inside a second vacuum chamber

called the cryostat. The systems operate at high vacuum conditions and at very different temperatures. The superconducting magnets in DEMO will be actively cooled by helium at about 4 K and enclosed between the hot vacuum vessel, with operational temperature of 200 °C, and the cryostat at room temperature. One of the key components protecting the magnets and mitigating the radiation heat transferred from the vacuum vessel and the cryostat are the thermal shields, which have to be placed on both sides of the magnet system. To effectively reduce thermal radiation, thermal shields should have surfaces with low emissivity and should be actively cooled in the temperature range between 80 K and 120 K [6–8]. Thus, the cryogenic cooling plant should overcome the heat loads on the two, magnets and thermal shields, cold DEMO systems. Thermal shields can be additionally covered with passive multilayer insulation, the objective of which is to reduce the radiation heat load on the thermal shields and, consequently, the refrigeration power needed to maintain the operating temperatures of the cold systems. The latter is an important design objective in DEMO to achieve efficient net electricity production. With this goal, the present work aims at the analysis of heat loads on the magnets and thermal shields as well as the estimation of the refrigeration power, considered of paramount importance for the design and efficiency of DEMO reactor.

⁎

Corresponding author. E-mail addresses: [email protected] (B. Končar), [email protected] (O. Costa Garrido), [email protected] (M. Draksler), [email protected] (R. Brown), [email protected] (M. Coleman). http://dx.doi.org/10.1016/j.fusengdes.2017.10.017 Received 27 July 2017; Received in revised form 16 October 2017; Accepted 24 October 2017 Available online 02 November 2017 0920-3796/ © 2017 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).

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Nomenclature

ta tfc tot ts vv vvts

Latin letters A L q Q R T

Surface, m2 Length, m Heat flux, W/m2 Heat flow, W Distance between surfaces, m Temperature, K

Thermal anchor Toroidal field coils Total Thermal shield Vacuum vessel Vacuum vessel thermal shield

Superscripts rad cnd

Radiation Conduction

Greek letters Acronims ε σ

Emissivity Stefan-Boltzmann’s constant, W/m2 K4

BLA CS CTS CR DEMO GS ITER MAG MLI PFC TFC TS VV VVTS

Subscripts amb c cr cts gs h mag mli net ss sup

Ambient Cold Cryostat Cryostat thermal shield Gravity support Hot Magnet system Multi layer insulation Net Stainless steel Support

Blanket Central solenoid Cryostat thermal shield Cryostat Demonstration power reactor Gravity supports International tokamak experimental reactor Magnet system Multi layer insulation Poloidal field coils Toroidal field coils Thermal shield Vacuum vessel Vacuum vessel thermal shield

working temperature of the thermal shields that minimizes the total refrigeration power required to actively cool the magnets and thermal shields. Analysis of static heat loads takes into account the thermal radiation between component surfaces and heat conduction between the components that are in physical contact. In terms of reducing thermal loading on components, the impact of multilayer insulation on both sides of the thermal shields is analysed and discussed. The numerical analysis of heat radiation is a time consuming process, hence an analytical modelling is used to perform a series of parametric studies for

In the complex DEMO tokamak machine, there will be additional contributors to the total refrigeration power such as superconducting current leads, cryo-pumps and cryo-distribution system loads [7,9]. These systems and design specific loads are not considered in this work, which focuses on the theoretical optimization of the DEMO thermal shields base concept. The underlying study provides the thermal analysis of integrated DEMO tokamak systems with two main objectives: first to predict thermal loading on the components and second to estimate the optimal

Fig. 1. CAD geometry of DEMO tokamak without port extensions, cryostat and thermal shields (left). Finite element model of 20° sector including thermal shields, simplified port extensions and the cryostat (right).

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2.1. Thermal radiation

optimization of thermal shields temperature. Reliable estimation of radiation heat loads at different operating conditions and thermal shields configurations is performed with the fit-for-purpose analytical model which has been prior compared and additionally validated with the finite element numerical simulations [10].

Due to the high vacuum and high temperature difference between the component surfaces, thermal radiation is the prevalent mode of heat transfer in the cryostat besides conduction. Thermal radiation exchange between the surfaces depends on their temperature, emissivity, size and orientation. The accuracy of radiative heat transfer prediction has been discussed in several works [18–20]. In particular, the correct evaluation of the surface orientation effect in complex geometry is a challenging task that requires complicated calculation of view factors [20,21]. In the current work, numerical simulations of thermal radiation are performed for the base case (Table 1) where the thermal shields temperatures are the same, Tts = Tcts = Tvvts, and Tvv = 473 K. After evaluation of numerical errors the simulations are compared with an analytical model which is corrected in the next step to take into account (conservatively) the simulation results. Since the numerical simulations are time consuming, the follow up parametric analyses in section 3 are performed solely with the analytical model.

2. Thermal model of DEMO thermal shields and magnets Preparation of the DEMO thermal model is based on the pre-conceptual CAD design [11], which includes the vacuum vessel with ports (VV), the in-vessel components, i.e. blankets (BLA) and divertor (DIV), and the magnet system (see Fig. 1, left). For the purpose of thermal analyses, both of the thermal shields (TS) enclosing the magnets, i.e. vacuum vessel thermal shield (VVTS) and the cryostat thermal shield (CTS), as well as the cryostat (CR) were designed on a rather simplified way [12]. Moreover, current design of the DEMO tokamak assembly consists of 18 toroidal sectors. Due to toroidal symmetry only one toroidal sector was modelled (Fig. 1, right). The present thermal analysis is focused on the evaluation of thermal loads applied on the thermal shields and superconducting magnets located in the interspace between the vacuum vessel outer walls and the cryostat. Both systems use cryogenic cooling loops for heat removal. The following modes of heat transfer need to be considered:

2.1.1. Numerical model The finite element (FE) code ABAQUS [10] was used to perform numerical analyses. The FE model of 1/18th of DEMO tokamak is presented in Fig. 1, right. The radiation heat exchange in the tokamak is simulated as a closed cavity thermal radiation problem [23]. Due to the toroidal symmetry, only the VV ports need to be closed by lids to form a completely closed geometry of the tokamak FE model. The problem formulation is based on grey body radiation theory and diffuse reflections between the surfaces are assumed. Each surface is composed of small elemental surfaces, termed as facets. In the cavity radiation formulation [10], the thermal radiation flux qirad [W/m2] into the cavity facet i (see Fig. 2) is defined as:

• Thermal radiation on the TS surfaces. • Thermal radiation on the magnet system, which includes toroidal field coils (TFC), poloidal field coils (PFC) and central solenoid (CS). • Heat conduction load on the TS through the TS supports. • Heat conduction load on the magnets through the attachments to the TS and through the TFC gravity supports.

Due to high vacuum inside the cryostat during normal operation, the heat transfer by convection can be neglected. The volumetric heating of the components due to neutron irradiation is also not considered in this study. Based on ITER data [13], the neutron heating increased the overall thermal load on thermal shields only by a small amount (less than 1%). The majority of the nuclear irradiation is being captured by the blanket and divertor with only a very small amount being transferred to the vacuum vessel [14,15] which provides the ultimate nuclear shielding of the superconducting magnets. As in ITER, neutron shielding plates are placed in the interspace between inner and outer shells of the VV, while the neutron heat is being removed from the VV by water also serving as a moderator In order to avoid regular vessel baking cycles at 200 °C (as required for the ITER VV operated at 70 °C) the DEMO VV is operated at 200 °C (473 K) [16]. In turn, this results in higher thermal radiation loads on thermal shields as discussed in the current concept. All components are actively cooled by the cooling pipes trying to establish approximately uniform heat removal from the component surfaces. For the purpose of the global thermal analysis the operating temperatures of the component surfaces are set as constant values. The adopted normal operation temperatures (base case), emissivities and component materials are listed in Table 1 [17,25]. The magnets are conservatively modelled as a black body with the emissivity of 1.

N

N

qirad = σεi ∑ εj ∑ Fij C −ji 1 (Tj 4 − Ti 4), j=1

k=1

where N represents the number of facets forming the cavity, εi and Ti represent the emissivity and the temperature of the facet i, σ is the Stefan-Boltzmann constant, Fij is the geometrical view factor matrix and Cji = δij − (1 − εi ) Fij is the reflection matrix with δij denoting Kronecker delta function. The dimensionless view factor Fij is purely a geometrical quantity defined as the fraction of the radiation leaving the facet dAi and intercepted by the facet dAj [23]:

Table 1 Operating temperatures of the components in the DEMO cryostat –base case. Component

T [K]

ε

Material

VV Magnets CTS, VVTS CR

473 4 80 293

0.25 1 0.05 0.25

SS-316 SS-316 SS-304 SS-304

(1)

Fig. 2. Radiation heat flux into a cavity facet [10].

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Fij =

1 Ai

∫Ai ∫Aj

cosθi cosθj πR2

dAi dAj ,

Table 2 Simulated radiation heat loads on 2015 CAD geometry [11] – base case from Table 1.

(2)

where R is the distance between the facets dAi and dAj, θi and θj are the angles between their normal vectors and R. For the closed cavity, very useful view factor relations are reciprocity (dAiFij = dAjFji) and sum-

Component

Surface [m2]

Qirad Net Heat Flow [kW]

N

⎛ ⎞ mation rule ∑ Fij = 1 [23]. The latter relation follows the con⎜ ⎟ ⎝ j=1 ⎠ servation requirement that all radiation leaving the surface i must be intercepted by some other surface j. In an open cavity this sum is always less than one, indicating that thermal radiation to the ambient takes place. Ideally, the total radiation heat exchange between all surfaces in a closed cavity should be equal to zero, ∑ Qirad = 0 where Qirad = Ai ·qirad denotes the thermal radiation flow (in Watts) into the surface Ai.

BLA DIV VV with ports/lids VVTS Magnets CTS CR Total

2.1.2. Numerical simulations and their accuracy Numerical errors in calculation of view factors in simple geometries can be evaluated by analytical expressions [21] or through the energy balance in more complex geometries. In the numerical simulation of thermal radiation in closed cavity, the energy balance is never fully preserved, mainly at the expense of numerical errors arising from spuriously calculated view factors. Taking this into account, a measure for the relative simulation error in the closed tokamak system can be defined as the ratio between the sum of all net radiative heat flows in the tokamak ∑ Qi and the average of all absorbed and emitted heat i

∑i ⎛⎜

∑i

⎝

Qirad Qirad

Received

Net

−916.4 −119.2 −495.8

3375.0 487.8 8510.5

−271.5 −244.3 −181.4

– – 123.2

−271.5 −244.3 −58.2

893.4 1.3 148.5 416.5 −71.7

7410.4 6552.1 4151.0 5517.2

−0.1 – −0.1 – Relative error −4.8%

121.1 0.2 35.4 7.5

121.0 0.2 35.3 75.5

2.1.3. Analytical thermal radiation model and results A simplified theoretical analysis has been performed to compare the theory and simulation results, ultimately, validating both models. The magnets (MAG) are enclosed between the VVTS and CTS. It is assumed that the hot VV emits thermal radiation entirely to the VVTS and the CTS intercepts the thermal radiation only from the cryostat (CR). This simplification of the more complex VV port conditions is described in the discussion of the results. The scheme of the theoretical model is shown in Fig. 3. In this model, each system of two opposing surfaces at different temperatures can be described as a two-surface enclosure, where the thermal radiation exchange occurs only with each other. The thermal radiation flux between the surfaces A1 and A2 at temperatures T1,T2 with emissivities ε1, ε2, can be expressed as:

⎞⎟/2 ⎠

Emitted

radiative heat flow. On the other side, the absorbed heat by the magnets is rather low (1.3 kW), proving the effective radiative heat shielding provided by the actively cooled thermal shields (VVTS, CTS) at 80 K. The values of emitted, absorbed and net heat fluxes qirad per specific component are provided in the last three columns of Table 2. It should be noted that all simulated heat fluxes (qirad ) in Table 2 are averaged across the surface of each component [25]. The VV with ports, for example, absorbs 123 W/m2 of thermal radiation flux from the blankets and divertor, while it emits about 181 W/m2 to the VVTS. In total, vacuum vessel is a net emitter (–58 W/m2).

flows (absolute values) exchanged in the tokamak system:

Relative simulation error =

qirad Heat Flux [W/m2]

(3)

Following the notation of Eq. (1), the negative value of Qi denotes that the surface Ai emits thermal radiation and the positive Qi denotes absorbed thermal radiation. To evaluate the accuracy of simulation results, the complete tokamak system is simulated although the heat loads on thermal shields and on magnets are the main focus of this study. Numerical mesh has a strong impact on the simulation accuracy. As reported in [24], the majority of the tokamak components are meshed with hexahedral elements, whereas tetrahedral elements are used only for meshing of regions where the ports are attached to the vacuum vessel [25]. The number of facets with erroneous view factors can be substantially reduced if sufficiently dense mesh with appropriate adaptation of mesh topology to the model geometry is applied [25]. The simulation of the base case, with actively cooled thermal shield temperature of 80 K (Table 1), resulted in the thermal radiation flows Qi provided in Table 2 for the full tokamak geometry. Taking into account that only a 20° sector of the tokamak is simulated, the results in Table 2 include the multiplication factor of 18 to obtain the radiation heat loads for the full tokamak geometry. Surface areas of individual components (third column of Table 2) are also provided for the full geometries. The magnet surface includes all outer surfaces of TFC, PFC and CS. For the sake of completeness and numerical error estimation, the heat flows of all components (including in-vessel components – blanket and divertor) are presented. The relative simulation error for the entire tokamak system, calculated using Eq. (3) is lower than 5%. The net thermal radiation flows Qirad on each component are given in the second column of Table 2. Recall that the positive net heat flow indicates that the component absorbs radiation from the surrounding surfaces, while the negative values indicate that the component is a net emitter. As expected, hot in-vessel components (BLA, DIV) and VV are net emitters whereas the thermal shields and magnets are net absorbers. The highest heat flow is absorbed by the VVTS since it encloses the entire VV. The cryostat and CTS also absorb a substantial amount of

qrad =

Qrad = A1

σ (T24 − T14 ) 1 ε1

+

(

1 ε2

)

−1

A1 A2

. (4)

Eq. (4) considers opaque grey surfaces with infinite number of

Fig. 3. Simplified thermal radiation scheme for the theoretical model.

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seen that the emitted heat fluxes from both thermal shields (VVTS and CTS) to the magnets are negligible compared to their absorbed radiation fluxes from the VV and cryostat, respectively. Theoretical predictions of thermal radiation to VVTS and magnets show fairly good agreement with the simulation results. Theoretical heat fluxes are up to 10% higher than simulated ones, thus they are on the conservative side. Some major discrepancies can be observed in the case of thermal radiation to the CTS, where the simulation result for the absorbed heat flux is almost twice the theoretical value. This is a consequence of the simplification in the latter, where the CTS surface at 80 K intercepts only the radiation from the cryostat surface at 293 K. In the model of the current DEMO design, the VV ports at 473 K are not completely shielded by the VVTS (see red circles in Fig. 4a) and therefore emit a significant portion of the heat to the interspace bounded by the CTS and the cryostat. The local concentration of high thermal radiation around the ports is clearly visible in Fig. 4b, showing the distribution of simulated thermal radiation flux on the CTS. Similar differences between analytical and simulated heat fluxes results are obtained when considering different thermal shield temperatures (Tts = 80, 120, 150 K), as can be observed in Fig. 5. The heat rad rad rad fuxes qvvts , qcts and qmag in Fig. 5 represents net thermal radiation on the VVTS, CTS and MAG components, respectively. Theoretical calculations are presented by full lines, whereas symbols denote simulations. These results therefore confirm that the theoretical model for thermal radiation on the CTS needs to be corrected in order to conservatively consider the modelling simplifications through the numerical simulation results. In the follow up analyses, the modified analytical model for thermal radiation is used, which employs the mathematical expressions of thermal flows as given in Table A.1 of Appendix. In the modified model, the thermal radiation on the CTS is taken into account by multiplying rad the theoretical values for the heat flow by a factor of 2 (Qcts in Table

Table 3 Comparison of simulation and theoretical results − base case. qrad Heat Flux [W/m2]

Component

Emitted Simul.

Absorbed Theory

Simul.

Net Theory

Simul.

Theory rad ) 123.20(qvvts

VVTS

−0.09

−0.11

121.10

123.30

121.00

MAG

–

–

0.18

0.20

0.18

CTS

−0.09

−0.11

35.40

18.10

35.30

rad ⎞ 0.20⎜⎛qmag ⎟ ⎝ ⎠ rad 17.90(qcts )

reflections between them and is valid for the case of convex shape of the inner surface A1. In this case all radiation leaving the inner surface A1 must reach the outer surface A2, hence the view factor from A1 to A2 isequal to 1. Thermal radiation flux absorbed by the magnets can be readily calculated by Eq. (4), where A1 represents their surface and A2 is the surface of enclosing thermal shields, VVTS and CTS. All surfaces used in the calculations are given in Table 2. Eq. (4) can be further simplified for large surfaces that are placed together at a close distance. Assuming equal surfaces with the view factor of 1 in both directions, the thermal radiation flux between the components can be approximated by that between the infinite parallel plates:

qrad =

σ (T24 − T14 ) 1 ε1

+

1 ε2

−1

. (5)

Eq. (5) is applied for the estimation of thermal radiation flux between the VV and VVTS and between the cryostat and CTS. Comparison of theoretical and simulation heat fluxes on the thermal shields and magnets for the base case (Table 1) is presented in Table 3. It can be

Fig. 4. Geometry of the DEMO Tokamak model (a). Distribution of the simulated thermal radiation flux (W/m2) on the CTS (b).

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Fig. 5. Comparison of theoretical and simulated radiation heat fluxes at varied thermal shields temperature.

as:

Table 4 Radiative heat loads for different VVTS temperatures.

Tts [K]

80 120 150

rad Qvvts

rad Qmag

[kW]

rad Qcts

[kW]

Qgscnd = Ags · [kW]

Simul.

Theory

Simul.

Theory

Simul.

Theory

893.4 887.3 876.9

912.8 906.3 894.5

1.3 5.4 13.9

1.3 6.8 16.6

148.5 144.8 138.9

149.5 144.1 134.5

kss (Tcr − Tta), Lgs

(6)

where Tta is the thermal anchor temperature, Lgs = 1.76 m is the conduction length between the pedestal ring and thermal anchor, kss = 14.8 W/mK is the average thermal conductivity of the flexible plates at cryostat temperature and Ags = 23.9 m2 is the total contact area of 18 DEMO gravity supports. The length and the conductivity have been adopted from ITER while the conduction area has been estimated from the ITER gravity supports based on the extrapolation of the DEMO TFC larger mass [27]. Similarly to the above, the heat conduction from the thermal anchors to TFC is calculated as:

A.1 and Table 4). Comparison of thermal radiation flows, rad rad rad (Qvvts , Qcts , Qmag ) between the modified analytical model and simulation at 3 different TS temperatures is shown in Table 4. 2.2. Heat conduction loads

cnd Qtfc = Atfc ·

Heat conduction always occurs through the supports and attachments when there is a physical connection between the components at different temperatures. Although the DEMO attachments are not designed yet, their effect can be evaluated on the pre-design level using the design solutions (materials, estimated contact areas and dimensions) from the ITER experience [26]. The following supports and attachments are considered for the estimation of the heat conduction loads on the magnets and thermal shields:

kta (Tta − Tmag ), Ltfc

(7)

where kta = 3.48 W/mK is the average heat conduction coefficient, Ltfc = 3.5 m the conduction length between the thermal anchor and the TFC, both adopted from ITER [28], and Atfc = 58.5 m2 the contact area between the supports and the DEMO TFC, also extrapolated from ITER

• TFC gravity supports (GS): the 18 TFC magnets are supported by

• •

gravity supports resting on the cryostat pedestal ring. To avoid direct contact between the GS and TFC, the ITER concept of actively cooled thermal anchor [5,27] is considered to reduce the heat conduction from the cryostat to the magnets (see Fig. 6). Thus, the role of thermal anchors in heat conduction is equivalent to that of thermal shields in heat radiation. Supports between VVTS and TFC: the VVTS are attached to the TFC. Supports between CTS and cryostat: the engineering design of the CTS consists of 3 parts (upper, lower and equatorial) supported separately [17].

2.2.1. Heat conduction through the gravity supports The schematic representation of conduction paths through the DEMO GS is shown in Fig. 6. The heat conducted through the GS from the cryostat pedestal ring, assumed at the same temperature as the cryostat, is partially removed by the actively cooled thermal anchor. The heat from the cryostat to the thermal anchor Qgscnd is, in fact, conducted through stainless steel flexible plates, which is a structural feature of the gravity support [22]. The total heat conducted through the 18 DEMO gravity supports to the thermal anchor can be calculated

Fig. 6. Schematic representation of heat conduction paths through the gravity support to the TFC [27].

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[27]. An energy balance of the thermal anchor in Fig. 6 gives the heat that needs to be removed from it as: cnd Qtacnd = Qgscnd − Qtfc .

Table 5 Heat conduction through the VVTS and CTS support elements.

(8)

sections, Qtacnd

is assumed as a part of the heat load on the TS In later cooling system, therefore Tta = Tts. For the temperatures of the base case given in Table 1, but assuming a variable temperature of the thermal shields Tts, the calculated conduction heat through the gravity supports are shown in Fig. 7. It can be seen that at lower Tts temperatures the majority of the conduction heat is removed through the thermal anchor Qtacnd and only a small amount remains to be transferred cnd to the TFC Qtfc . With increased temperature Tts, the conduction heat to cnd increases linearly while the heat conduction to the the magnets Qtfc cnd at approxithermal anchor Qtacnd decreases and is surpassed by Qtfc mately 190 K.

Support elements

Th [K]

Tc [K]

Q cnd [kW]

VVTS supports CTS supports

80 293

4 80

0.2 1.5

Qicnd = Asup, i ⋅

1 ⋅ Li

Th

∫Tc

ki (T ) dT ,

(9)

where Asup,i is the contact area of the support element i, Li is the conki (T ) dT is the integral of the temperature deductive length and pendent thermal conductivity of the material [29]. Different materials are used for different type of supports. Details on materials, number and dimensions of support elements as well as detailed calculations of heat conduction are given in [17]. Table 5 summarizes total heat conduction

∫

n

⎛ ⎞ cnd cnd ) suploads ⎜Q cnd = ∑ Qicnd⎟ through the VVTS (Qvvts ) and CTS (Qcts i=1 ⎝ ⎠ port elements in the base case (Table 1). Heat conduction through the VVTS and CTS supports at varied thermal shields temperature Tts is shown in Fig. 8. The heat conducted cnd through the VVTS supports Qvvts increases with Tts as it contributes to the cnd magnets heat load. The conduction heat through the CTS support Qcts decreases contributing to the CTS heat load. In general, the heat conducted through the thermal shields supports is by order of magnitude lower than the heat conduction transferred through the gravity supports (see Fig. 7).

2.2.2. Heat conduction through the thermal shield attachments The supports of VVTS and CTS differ in their materials, lengths and contact areas, depending on the components where different parts of either VVTS or CTS are attached to. The estimation of heat conduction loads through the VVTS and CTS supports is based on the ITER design solutions [26] using the following assumptions:

• The number of supports and their adopted conduction lengths are assumed the same as in ITER. • The adopted material of DEMO supports is the same as in ITER case [26]. • The adopted contact areas of the attachments for DEMO are extra-

2.3. Total heat loads on thermal shields and magnets

polated from the ITER case taking into account the larger mass of the DEMO thermal shields [17].

Thermal radiation and heat conduction represent the total static heat loads on the structural components. The total heat loads on magnets and both thermal shields, VVTS and CTS, are presented here through the energy balance on the components, considering the heat load contributions evaluated in sections 2.1 and 2.2. The total heat load rad on the magnets includes the contributions from thermal radiation Qmag , cnd heat conduction through the TFC gravity supports Qtfc and heat concnd duction through the VVTS supports Qvvts :

The VVTS fully surrounds the VV and its ports up to the CTS (Fig. 4). The inboard and outboard parts of the VVTS are attached to the TFC by different supports and, thus, transferring conduction heat from the VVTS to the cold magnets. In the current thermal analysis, the three parts of the CTS (upper, lower and equatorial CTS) are supported separately while sharing the same temperature, Tts [17]. Upper CTS is attached to the cryostat top lid, lower CTS is supported by the cryostat pedestal ring and equatorial CTS is attached to the VVTS ports. No heat conduction needs to be considered in the latter since the CTS and VVTS temperatures are assumed equal. Contrary to VVTS supports, the conduction heat through the CTS supports is transferred towards the CTS. For the i-th VVTS or CTS support, the heat conduction between the hot Th and cold Tc sides can be calculated as:

rad cnd cnd Qmag = Qmag + Qtfc + Qvvts .

(10)

rad The total heat load on the VVTS consists of thermal radiation Qvvts cnd , and the heat conducted through the VVTS supports to the magnets Qvvts which reduces the previous:

rad cnd Qvvts = Qvvts − Qvvts .

(11)

The contributions to the total heat load on the CTS are thermal Fig. 7. Heat conduction distribution through the GS at varied temperature of the thermal shields Tts.

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Fig. 8. Heat conduction through the VVTS and CTS supports.

VVTS is exposed to the highest thermal radiation from the hot vacuum vessel. The attachment between the VVTS and TFC conducts a small amount of heat (0.2 kW) also to the magnets. The CTS intercepts thermal radiation from the cryostat and from the part of the VV ports protruding out of the CTS. The heat conduction to the CTS represents approximately 20% of the total heat load to the CTS, mainly due to that through the GS to the thermal anchor Qtacnd , At the low thermal shields temperature of 80 K the heat conduction through the TFC gravity cnd supports Qtfc represents a major contribution to the total heat load on the magnets. Variation of thermal radiation and heat conduction flows over the range of thermal shield temperatures Tts is presented in Figs. 9 and 10. For both heat transfer modes the heat flow to the thermal shields and magnets decreases and increases with increased Tts, respectively. It may rad be observed that the thermal radiation to the VVTS Qvvts represents by far the largest heat load contribution. In Fig. 10, the heat conduction to cnd cnd cnd the magnets is calculated as Qmag and the combined heat = Qtfc + Qvvts cnd conduction to both thermal shields as Qtscnd = Qtacnd + Q cnd cts − Qvvts (see Table 6). Variation of the total heat load on thermal shields and magnet system is shown in Fig. 11. It can be seen that the heat load on the VVTS, Qvvts , presents the highest contribution to the total heat load Qtot .

Table 6 Estimated total heat loads on magnets, VVTS and CTS due to thermal radiation and heat conduction (base case). Component

Thermal radiation [kW]

Heat conduction [kW]

Total heat to be removed [kW]

VVTS

rad ) 912.8 (Qvvts

cnd ) −0.2 (Qvvts

912.6 (Qvvts )

Magnets (total)

rad ) 1.3 (Qmag

cnd ) 4.6 (Qmag

5.9 (Qmag )

– from thermal anchor

/

– from VVTS supports CTS (total)

/

– from GS – from CTS supports Total

cnd ⎞ 4,4 ⎛⎜Qtfc ⎟ ⎝ ⎠ cnd 0.2 (Qvvts )

rad (Qcts ) /

39.9

/

cnd ) 1.5(Qcts

1,063.6

44.3

189.4 (Qcts )

cnd ) 38.4 (Qta

1,107.9 (Qtot )

rad , heat conduction through the GS to the thermal anchor radiation Qcts cnd : Qtacnd and heat conduction through the CTS support elements Qcts rad cnd Qcts = Qcts + Qtacnd + Qcts .

(12)

The total heat load that needs to be removed by the refrigeration system thus amounts to:

Qtot = Qrad + Qvvts + Qcts .

3. Estimation of optimal TS design temperature – parametric analysis

(13)

Heat loads on the thermal shields and superconducting magnets have to be removed through the cryogenic system that shall provide

Separate contributions and total heat loads on thermal shields and magnets for the base case with Tts = 80 K are compiled in Table 6. The

Fig. 9. Thermal radiation loads at varied temperature of the thermal shields.

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Fig. 10. Heat conduction loads at varied temperature of the thermal shields.

Fig. 11. Total heat loads at varied thermal shields temperature.

Fig. 12. Influence of thermal shield temperature on the theoretical refrigeration power for the base configuration of thermal shields. Optimal design temperature is determined at minimum total refrigeration power.

helium cooling at different temperature levels. Magnets need to be kept around 4 K and the thermal shields need to be cooled to the temperatures approximately between 80 K and 120 K [6]. Considering the fixed temperature of the cold magnets it is very useful to investigate the optimum operating temperature of thermal shields already at their early development stage. Taking into account that the magnet heat load Qmag increases and the heat load on both thermal shields (Qvvts, Qcts)

decreases with increased thermal shields temperature Tts (see Fig. 11), an optimal Tts can be found where the overall refrigeration power is minimized, which in turn would allow for a higher net electricity production of the DEMO plant. At the pre-design stage, the Carnot factor can be used to evaluate the theoretical refrigeration power. The Carnot factor, (Tamb − Tc )/ Tc , defines the minimum refrigeration power needed to extract the heat at 46

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The calculated heat loads and theoretical refrigeration powers, Eq. (14), given in Table 8 are obtained at the optimum thermal shields temperature representative of the single operating point where the total refrigeration power, Ptot, is minimized. The results from Table 8 are analysed in detail in the following sections.

Table 7 Parametric cases investigated in the study.

Base case Varied TVV Inclusion of MLIs

Case Case Case Case Case Case Case

1 2 3 1–1 1–2 1–3 2–3

TVV [K]

VVTS-MLI

CTS-MLI

473 373 423 473 473 473 373

/ / / / 1 MLI 1 MLI 1 MLI

/ / / 1 MLI / 1 MLI 1 MLI

3.1. Effect of VV operation temperature The effect of vacuum vessel temperature on Ptot is shown in Fig. 13. Reduced VV temperature significantly decreases the total power and shifts the optimum TS temperature towards the lower values. Reducing of VV temperature from 473 to 373 K (Case 2) decreases the total power by 35% and shifts the optimum Tts temperature from 123 K to 104 K. The main reason is the reduced radiative heat load on the VVTS (see Fig. 14).

a cold temperature Tc and reject it a higher ambient temperature Tamb (293 K in our case) [30]. It should be noted, that the refrigeration power in real systems is always higher than the theoretical refrigeration power based on the Carnot factor due to the inevitable entropy losses in the process (compression, expansion). The theoretical powers for the cryogenic cooling of VVTS, CTS and magnets are calculated as follows [12]:

Pvvts = Q vvts⋅

The characteristics of radiative multilayer insulation (MLI) package are adopted from the thermal insulation data for Wendelstein 7-X [31], where one passive MLI package consists of 20 layers with an overall thermal conductivity of 0.1 W/mK. The adopted thickness of one MLI package is 15 mm [31]. In the presented analysis, MLIs are added either on the warm side of CTS or on the warm side of VVTS. Analytical expressions for the thermal radiation flows and the equilibrium temperatures of passive MLI for different considered cases are listed in Appendix (Table A.2). In the calculation procedure it is adopted that the emissivity of MLI package is the same as the emissivity of the CTS and VVTS. Only thermal radiation between the MLI and the neighbouring surfaces is assumed, while the heat conduction due to physical attachments is neglected. The relative emissivity between the MLI and actively cooled CTS or VVTS then amounts to:

(Tamb − Tts ) , Tts

Pmag = Qmag⋅ Pcts =

3.2. Effect of radiative MLI insulation

(Tamb − Tmag ) Tmag

,

−T ) (T Qcts⋅ ambT ts , ts

Ptot = Pvvts + Pmag + Pcts ,

(14)

where Pvvts, Pmag, Pcts and Ptot denote theoretical refrigeration power of VVTS, MAG, CTS and total power, respectively. Here the cold temperatures denote the constant temperatures of the cooled components. The variation of refrigeration power with the TS temperature for the base case configuration of thermal shields (actively cooled without multilayer insulation) and VV temperature of 473 K is shown in Fig. 12. The refrigeration cost of magnet cooling at 4 K is much higher than that of the thermal shields, as the Carnot factor is much higher at 4 K (factor 72.2) than for example at 80 K (2.6). Therefore, the refrigeration power for the magnets is rapidly growing with the increase in TS temperature. At the same time the refrigeration power for both thermal shields decreases much more slowly. As shown in Fig. 12, the total refrigeration power reaches a minimum at the optimal Tts of 123 K. In the pre-conceptual DEMO design phase, the assumed VV operating temperature is still preliminary, therefore its effect on the overall refrigeration power is studied next. Additionally, the radiation heat load on the actively cooled thermal shields can be further reduced by inclusion of passive Multi-Layer Insulation (MLI) packages on the warm side of VVTS or CTS. Parametric studies listed in Table 7 include cases with different VV temperatures and TS configurations that, in addition to active thermal shields, also include packages of passive MLI. Case 1 represents the base case considered so far with Tts = Tcts = Tvvts and TVV = 473 K with no MLI. The impact of VV operating temperature is analysed in Cases 2 and 3 and the effect of additional MLI insulation is investigated in Cases 1–1 to 2–3.

εmli = 1/(2/ εcts − 1).

(15)

Taking into account that the emissivities of the CR and VV are equal to 0.25 and the emissivity of the MLI is equal to the emissivity of both thermal shields (0.05), a single relative emissivity ε1 can be defined applying to thermal radiation between the VV and VVTS (or MLI) and between the CR and CTS (or MLI):

ε1 = 1/(1/ εcr + 1/ εcts − 1).

(16)

The effect of MLI at varied Tts is shown in Fig. 15. The results show that adding MLI on the CTS side (Case 1–1) has no significant impact. The effect of MLI on the side of VVTS (Case 1–2) is far more important since the total heat load and consequently the refrigeration power is dominated by the thermal radiation from the vacuum vessel. The effect of MLI on the VVTS side is comparable to the reduction of VV temperature by 100 K (see Case 2 in Fig. 13) resulting in reduction of the total power Ptot by 35% and shift of the optimal TS temperature to 104 K (see Table 8 and Fig. 15). Addition of MLIs on both thermal shields (Case 1–3) further reduces the Ptot, but the impact of additional

Table 8 Results of parametric cases at optimal thermal shields working temperature Tts. Tts(opt) [K]

Qvvts [kW]

Qmag

Pvvts [kW]

Qcts [kW]

[kW]

Qtot

Pmag [kW]

Pcts [kW] Ptot [kW]

[kW] Case Case Case Case Case Case Case

1 2 3 1–1 1–2 1–3 2–3

123.0 104.0 113.0 120.0 104.0 99.0 84.0

905.4 349.0 578.5 906.3 336.0 336.5 129.8

14.9 10.0 12.1 14.0 10.0 9.0 6.5

172.0 180.7 176.8 81.3 180.7 89.0 93.9

1,092.3 539.7 767.3 1,001.6 526.6 434.6 230.2

1,251.4 634.3 921.4 1,306.5 610.6 659.5 322.9

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1,074.7 722.2 872.6 1,009.8 722.2 649.7 471.7

237.8 328.3 281.6 117.2 328.3 174.5 233.6

2,563.9 1,684.8 2,075.7 2,433.6 1,661.1 1,483.6 1,028.2

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Fig. 13. Effect of VV operating temperature on total refrigeration power and optimal thermal shields temperature.

Fig. 14. Thermal radiation to VVTS: effect of VV operating temperature.

Fig. 15. Total refrigeration power: effect of MLI radiative insulation.

4. Conclusions

MLI on the CTS side is small comparing to the previous. The addition of MLI on the VVTS side is therefore highly beneficial for an improved efficiency of the DEMO cryogenic cooling system. The combined effect of lower VV temperature and addition of MLIs on both thermal shields (Case 2–3) is also presented in Fig. 15 resulting in the lowest Ptot. Compared to the base case, the total refrigeration power is reduced even by 60% at the optimal TS temperature of 84 K.

The initial thermal shield concept based on the current DEMO baseline design has been analysed focusing on static heat loads and optimisation of thermal shields design temperature. Total heat loads on thermal shields and superconducting magnets was evaluated. Thermal radiation on the VVTS presents by far the largest contribution to the total heat load on thermal shields and magnets (more than 80%). Consideration of heat conduction through 48

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the physical support affects mostly the magnets, where the majority of the conductive heat is transferred through the TFC gravity supports. Heat conduction load on the CTS contributes approximately 20% of the total heat load to the CTS at the TS temperature of 80 K, but becomes less important at higher TS temperature. In this study, the optimal TS design temperature corresponds to the minimum theoretical refrigeration power for cooling of the TS and the magnets. Parametric studies on VV operating temperature and MLI have been performed to optimize the TS working temperature and evaluate its impact on the theoretical efficiency of the cryogenic system. It is shown that CTS refrigeration power has a small influence on the total refrigeration power, therefore the inclusion of MLI on the CTS side does not bring substantial reduction of the total power. The results of the parametric analyses indicated that the decrease of VV temperature and inclusion of MLI on the warm VVTS side have the greatest effect on reducing the total refrigeration power. It is demonstrated that the effect of one MLI on the VVTS side is comparable to the effect of reducing the VV temperature from 473 K to 373 K. Comparing to the base case (without MLI), the thermal load on the VVTS is reduced from about 900 kW to roughly 330 kW. At the same time the total theoretical refrigeration power is reduced from about 2.5 MW to approximately 1.5 MW with the optimal TS temperature shifted from 80 K to higher temperatures of about 100 K. Acknowlwdgements This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. The financial support from the Slovenian Research Agency (research core funding No. P2-0026 “Reactor engineering”) is also acknowledged. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.fusengdes.2017.10.017. References [1] C.C. Baker, R.W. Conn, F. Najmabadi, M.S. Tillack, Status and prespects for fusion energy from magnetically confined plasmas, Energy 23 (1998) 649–694. [2] C. Bachmann, et al., Initial DEMO tokamak design configuration studies, Fusion Eng. Des. 98–99 (2015) 1423–1426. [3] G. Federici, C. Bachmann, W. Biel, et al., Overview of the design approach and prioritization of R & D activities towards an EU DEMO, Fusion. Eng. Des. 109–111 (2016) 1464–1474.

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