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Analyses of temperature transients in ITER design concepts following hypothetical loss of cooling accidents
Fusion Engineering and Design 54 (2001) 413– 419 www.elsevier.com/locate/fusengdes
Analyses of temperature transients in ITER design concepts following hypothetical loss of cooling accidents W.E. Han Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB, UK
Abstract Bounding calculations of thermal transients following a hypothetical (Category V) loss of coolant accident in two international thermonuclear experimental reactor (ITER) design options, EU-I and ITER-fusion energy advanced tokamak (FEAT), have been carried out for a variety of assumptions concerning heat-transfer to and heat rejection from, the cryostat. It is shown that, even when unrealistically conservative assumptions are made in illustrative calculations, the temperatures do not approach melting point for any part of the plant structure. In all cases, maximum temperatures are reached within 1 year. It is also concluded that for the baseline scenario for ITER-FEAT in which helium gas is assumed to be present in the cryostat, convectively transferring heat between components, the outboard first-wall temperature never exceeds 530°C. A significant improvement could still be made if the surface emissivity of the thermal shields could be increased by some means during the post-accident period. © 2001 Published by Elsevier Science B.V. Keywords: ITER; Accidents; Design concepts
1. Introduction As part of the assessment of the safety performance of two design concepts for a burning plasma experiment, we describe bounding calculations of temperature transients for a hypothetical beyonddesign-basis (Category V) type accident in the proposed EU-I and International Thermonuclear Experimental Reactor-Fusion Energy Advanced Tokamak (ITER-FEAT) designs. These designs have evolved since the first Engineering Design Activities (EDA) phase of ITER concluded in July 1998, with its final design report (FDR) specifying E-mail address: [email protected] (W.E. Han).
a device, which is now known as ITER-FDR. Following that phase, there was an immediate exploration of options for a smaller alternative, which would involve reduced costs and also meet reduced technical objectives. A range of alternatives were defined, following which two further concepts (EU-I and ITER-FEAT) were further developed. The main parameters of these two concepts are compared with Table 1. They are broadly similar but further developments are likely to be based on ITER-FEAT. The hypothetical accident scenario is a complete loss of all active cooling from all systems for an indefinite period of time, as a bounding case. The calculations of resulting temperature transients are performed using CULTRAN [1], a code
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which models the radial heat-transfer in the structure of a fusion power plant in 1-D cylindrical geometry, based on dimensions applying to the radial build at the toroidal midplane. In this model, the main components are represented as homogeneous cylindrical layers. Although this approach does not take into account the toroidal spacing between individual toroidal field coils, the resulting simplification has a conservative impact on the temperature transient calculations. Each cylindrical layer may either be in thermal contact with a neighbouring one or separated from it by a gap. If there is a gap, heat-transfer across the gap may occur either through radiation or through use of a heat-transfer coefficient, in proportion to the temperature difference between the two surfaces. The only heat source assumed to drive the temperature excursions is the decay-heat of plant structures. This decay-heat data was obtained from calculations which assumed that all components had received the maximum possible operational irradiation history, which covers a period of about 10 years. The divertor was not modelled, although CULTRAN has the capability to do this when data is available for this component. 2. EU-I calculations The EU-I radial build specified by Daenner [2] was used in the CULTRAN model. Some of the scenario variations analysed in the thermal transient calculations relate to the outermost component included in the model, which is the cryostat comprising a concrete bioshield with internal steel liner. A gap between the liner and the concrete allows for the potential of a cooling flow of air, driven by natural convection, to remove heat from the liner. When this convective cooling is being modelled there is no need to take account of the concrete bioshield which is then omitted. If no convective cooling is assumed, then the less efficient alternative of conductive heat loss through the concrete bioshield is modelled. Some of the materials compositions for some EU-I components were provided by Cepraga [3], who also gave the decay-heat values used [4,5]. The crucial factors affecting post-accident temperature evolution are those relating to heat-
transfer between vacuum vessel and magnets, between magnets and cryostat, and heat removal from the cryostat. If there is no gas within the cryostat, then heat-transfer across any gaps must occur radiatively but, if gas (i.e. air or helium) is allowed in, then we need to account for the possibility of convective heat transfer. The convective case is dealt with by employing heat transfer coefficients of 1.3 and 2.3 Wm − 2 K − 1, depending on whether the gas is air or helium, respectively. These values were as used by Bartels in CHEMCON analyses [6], arising from assessments by Iseli [7] of thermal transport across thermal shields in ITER. Different cases were analysed to reflect different scenarios and to explore sensitivity to variations in assumptions made but, in view of the diminished interest in EU-I, we will look here at only two cases corresponding to the most benign and the most severe sets of assumptions for which the calculations were performed.
2.1. Helium in cryostat We take account of the effects of convective cryostat cooling, although neither the cryostat nor the bioshield are explicitly included in the calculation. This is accomplished by applying a heattransfer coefficient of 2 Wm − 2 K − 1, with respect to ambient temperature, to the outer surface of
Table 1 Comparison of main parameters of EU-I and ITER-FEAT concepts EU-I R (m) A (m) Ip (MA) B0 (T) Aspect ratio q95 Peak toroidal field (T) Toroidal field energy (GJ) Fusion power (MW) Mean neutron wall loading (MW m−2)
5.48 1.72 13.0 5.16 3.18 3.0 11.8 29 530 0.8
ITER-FEAT 6.20 2.0 15.0 5.3 3.10 3.0 11.8 41 500 0.57
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Fig. 1. Upper-bound temperature history, following loss of all cooling, in the outboard components of the EU-I model for the case of helium in the cryostat. The lower curve represents the magnets. Above this, the curves for fronts and backs of vacuum vessel, blanket and first-wall are also plotted and, after around 10 days, are seen to span a narrow range.
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bioshield was included, but there was no assumption of cooling flow behind the liner. Convective heat-transfer in air between vacuum vessel and magnets (heat-transfer coefficient of 1.3 Wm − 2 K − 1) was assumed. The magnet surface emissivity was taken to be 0.05 (based on safety and environmental assessment of fusion power (SEAFP) studies [8] in the absence of specific EU-I data), and heat-transfer between magnets and cryostat was by radiation. Although, this is not a fully consistent set of assumptions, the modelling of the heat-transfer between magnets and cryostat in this way was undertaken to add extra conservatism to the calculation. The results of this calculation appear in Fig. 2, showing the maximum first-wall temperature of about 630°C being attained at around 1 year.
3. ITER-FEAT calculations the magnets in the CULTRAN model. It was confirmed through auxiliary calculations that this gave a reasonable simulation of what would happen if the cryostat steel liner had been included and there had been a cooling flow of air due to natural convection at its outer surface, removing heat at the rate of 4 Wm − 2 K − 1. The prescribed heat-transfer coefficient of 2.3 Wm − 2 K − 1 was used to model convective heat-transfer in helium between vacuum vessel and magnets. The temperature histories, obtained from the CULTRAN calculations, of the outboard components appear in Fig. 1. The uppermost curve represents the first-wall temperature and it can be seen that at the end of the calculation (about 83 days), the first wall temperature is about 330°C. Note that temperatures are still rising gently at this point in time.
The source of the design data is reference [9]. As prescribed in this document, a safety factor of 1.2 was applied to the decay-heat values given.
2.2. No cooling flow inside liner
Fig. 2. Upper-bound temperature history, following loss of all cooling, in the outboard components of the EU-I model for the case of no convective cooling of the cryostat liner. At the end of the calculation, the component temperature histories appear in the following temperature order (starting with the lowest temperature); (1) Back of bioshield; (2) cryostat and front of bioshield, (3) magnets. Above these, the temperatures of fronts and backs of vacuum vessel, blanket and first-wall are also plotted, and are seen to span a narrow range.
This calculation (the worst case analysed) was performed to illustrate the consequences of an extreme set of assumptions and, in order to assess their potential severity, was continued until all components had reached their maximum temperature. For this scenario, the cryostat with concrete
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Again, a number of scenarios were analysed, and the presence of either helium or air in the cryostat was modelled with the same heat-transfer coefficients as those used in the EU-I calculations for heat-transfer to and from the magnets. In this design, there is a steel cryostat and concrete bioshield separated by a gap, allowing the potential for a similar cooling flow of air to that which might occur behind the cryostat liner in the EU-I design. To simulate this convective cooling of the cryostat, we follow the procedure used in reference [6] and apply the heat removal rate of 4 Wm − 2 K − 1 relative to ambient temperature (taken to be 300 K). Calculations were performed for four different scenarios. The first three included the convective heat removal from the outer surface of the steel cryostat and corresponded to the three cases of helium, air, or no gas within the cryostat. The fourth did not include the cooling of the cryostat with natural convection air flow and did not assume the presence of gas in the cryostat. This is the order in which the results are presented.
3.1. Helium in cryostat We apply the convective heat removal rate of 4 Wm − 2 K − 1 to the outer surface of the cryostat. Thus, we do not model the concrete bioshield. We assume a heat-transfer coefficient of 2.3 Wm − 2 K − 1 between vacuum vessel and magnets, and between magnets and cryostat. The calculated temperature histories of outboard components for this case are shown in Fig. 3. It can be seen that the peak first-wall temperature is about 530°C, occurring after around 8 months. Inspection of those curves also reveals that the main barriers to heat rejection are the thermal shields and cryostat heat removal rate.
3.2. Air in cryostat Again the concrete bioshield is not modelled and, instead, we apply heat removal at the rate of 4 Wm − 2 K − 1 at the outer surface of the cryostat. This time we assume a heat-transfer coefficient of 1.3 Wm − 2 K − 1 between vacuum vessel and magnets, and between magnets and cryostat.
Fig. 3. Upper-bound temperature history, following loss of all cooling, in the outboard components of the ITER-FEAT model for the case of helium in the cryostat. At the end of the calculation, the component temperature histories appear in the following temperature order: (1) cryostat 122°C, (2) back of magnets 287°C, (3) front of magnets 308°C. Above these, the temperatures of fronts and backs of vacuum vessel, blanket and first-wall are also plotted, and are seen to span a narrow range.
The results can be inspected in Fig. 4, which shows that the behaviour is similar to the helium case and, again, the main barriers to heat rejection are the thermal shields and cryostat heat removal rate. However, maximum temperatures are a little higher, with the first-wall peaking at about 675°C in around 11 months.
3.3. No gas in cryostat This is the third scenario in which the concrete bioshield is not modelled and in which we apply heat removal at the rate of 4 Wm − 2 K − 1 at the outer surface of the cryostat. However, as there is assumed to be no gas within the cryostat, heattransfer between vacuum vessel and magnets is via radiation through the thermal shield, modelled as a single layer, with emissivity on both surfaces assumed to be 0.03. This is based on information given in reference [9]. The thermal shield between magnets and cryostat is also modelled with these properties. The results of these calculations appear in Fig. 5, which shows that the in-vessel components become hotter than in the earlier calculations,
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with the first-wall peak temperature of around 730°C occurring in around 9 months. It can be seen that the thermal shields are now even more of a barrier to heat rejection as there is no convectively aided heat-transfer within the cryostat in this scenario. However, it can also be seen that the cryostat remains relatively cool. Hence, we may conclude that the value of the heat removal rate assumed from this component is of lesser importance, when there is no gas in the cryostat.
3.4. No cryostat con6ecti6e heat remo6al This is the worst case. This is similar to the earlier case in that there is assumed to be no gas within the cryostat. Hence, heat-transfer to and from the magnets is, again, through the thermal shields via radiation at the surfaces, with emissivity on both surfaces of each shield assumed to be 0.03. However, the concrete bioshield is modelled this time and the cryostat can now only lose heat by radiating to the inner surface of the concrete, which is a poor conductor. Note that inclusion of the bioshield accentuates the inability of cylindrical geometry to accurately represent the three-di-
Fig. 4. Upper-bound temperature history, following loss of all cooling, in the outboard components of the ITER-FEAT model for the case of air in the cryostat. At the end of the calculation, the component temperature histories appear in the following temperature order: (1) cryostat 111°C, (2) back of magnets 367°C, (3) front of magnets 384°C. Above these, the temperatures of fronts and backs of vacuum vessel, blanket and first-wall are also plotted, and are seen to span a narrow range.
Fig. 5. Upper-bound temperature history, following loss of all cooling, in the outboard components of the ITER-FEAT model for the case of no gas in the cryostat. At the end of the calculation, the component temperature histories appear in the following temperature order: (1) cryostat 102°C, (2) back of magnets 404°C, (3) front of magnets 523°C, (4) front of magnets 537°C, (5) thermal shield 624°C. Above these, the temperatures of fronts and backs of vacuum vessel, blanket and first-wall are also plotted, and are seen to span a narrow range.
mensional nature of the problem. The effect of this is to introduce even more conservatism into the results. It is evident from the temperature histories, shown in Fig. 6, that the first-wall, peaking at around 745°C in around 10 months, is only hotter by about 15°C compared with the earlier case with convective cryostat cooling. This is a very modest increase, despite the fact that the cryostat maximum is now around 140°C hotter. It would seem that, when there is no gas in the cryostat, the temperature histories of the in-vessel components are not greatly dependent on the variations we have explored concerning details of the cryostat/bioshield heat-rejection. Whether or not cryostat convective cooling is assumed, the cryostat temperature adjusts to that required to achieve matching of total decay-heat production and heat-rejection when component temperatures are reaching a plateau at around 10 months. Thus, although there is a large temperature drop across the bioshield, this does not allow us to conclude that it is a significant heat barrier in this particular case. Comparison with the earlier sce-
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nario indicates that even if the cryostat were maintained at ambient temperature it could not significantly alter the behaviour of the first-wall temperature as it is actually the thermal shields which are the main barriers to heat removal if there is no gas in the cryostat.
4. Discussion and conclusions EU-I and ITER-FEAT results are broadly similar and do not appear to be sensitive to factors relating to heat-transfer in first-wall and blanket regions. The presence of helium in the cryostat gives the best conditions for heat removal but, even with this benefit, estimates based on these calculations suggest that heat removal could be significantly enhanced and substantial reductions in maximum temperatures achieved, if surface emissivities of the thermal shields were to greatly exceed 0.05. Unfortunately, the aim of designing effective thermal shielding conflicts with the need for heat rejection in the event of a hypothetical loss of coolant. However, dramatic improvements
might be achieved using designs which degrade, following moderate temperature excursions, to give higher emissivity characteristics. Such a shield design has been assumed in SEAFP studies [8]. There the thermal shield was constructed from multiple layers of metalised plastic foil needing only a modest temperature rise in order to melt. It has been established that, even when making the most extreme assumptions, the maximum outboard first-wall temperature of around 745°C occurs at about 1 year after the loss of coolant. Thus, for all cases considered, temperatures remain far below melting point for any of the plant structures. Furthermore, the scenarios which do not include gas in the cryostat should be viewed as highly unrealistic since continuous pumping effort is required to exclude the air. The worst case calculations should therefore be viewed as illustrative only. In the case of ITER-FEAT, the presence of helium, as opposed to air, in the cryostat lowers maximum temperature by around 145°C and it is reasonable to assume that this would be introduced into the cryostat to reduce the accident consequences, by operator action, within the first day. This should be regarded as the base case scenario. More accurate calculations will be possible with a three-dimensional model of the designs. Work is under way to do this at Culham. Computational fluid dynamics will also allow the heat-transfer associated with natural convection flows within the plant to be simulated. Acknowledgements This work was funded by the UK Department of Trade and Industry and EURATOM.
Fig. 6. Upper-bound temperature history, following loss of all cooling, in the outboard components of the ITER-FEAT model for the case of no gas in the cryostat and no cryostat convective cooling. At the end of the calculation, the component temperature histories appear in the following temperature order: (1) back of bioshield 27°C, (2) front of bioshield 209°C, (3) cryostat 253°C, (4) thermal shield 463°C, (5) back of magnets 547°C, (6) front of magnets 561°C, (7) thermal shield 641°C. Above these, the temperatures of fronts and backs of vacuum vessel, blanket and first-wall are also plotted, and are seen to span a narrow range.
References [1] W.E. Han, N.P. Taylor, Calculations of temperature and mobilisation evolution for postulated accidents in SEAFP plant models., in: Proceedings of the 18th Symposium on Fusion Technology, Karlsruhe, Germany, 22 – 26 August 1994, Elsevier, Amsterdam, 1995, p. 1493. [2] W. Daenner, EU-I Radial Build Level 2, note forwarded by W. Gulden on 20 April 1999.
W.E. Han / Fusion Engineering and Design 54 (2001) 413–419 [3] [4] [5] [6]
D. Cepraga, private communication, 7 May 1999. D. Cepraga, private communication, 18 May 1999. D. Cepraga, private communication, 15 September 1999. H.-W. Bartels, Preliminary assessment of decay-heat in RC-ITER, ITER internal report, S81 RI 28 98-10-08, version 4, 12 February 1999. [7] M. Iseli, Heat transfer between VV, thermal shield and magnets with air or helium atmosphere in the cryostat, N
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80 MD 2 96-09-19, ITER NAKA JWS, September 1996. [8] N.P. Taylor, I. Cook, C.B.A. Forty, W.E. Han, P. Taylor, SEAFP-2 bounding accident analyses, Proceedings of the sixth IAEA Technical Committee Meeting on Fusion Power Plant Design, 23 – 27 March, Culham, Oxfordshire, 1998. [9] H.-W. Bartels, L. Topilski. (Eds.), Safety Analysis Data List-3 (SADL-3), Version 1.0, 29 February 2000.
Analyses of temperature transients in ITER design concepts following hypothetical loss of cooling accidents W.E. Han Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB, UK
Abstract Bounding calculations of thermal transients following a hypothetical (Category V) loss of coolant accident in two international thermonuclear experimental reactor (ITER) design options, EU-I and ITER-fusion energy advanced tokamak (FEAT), have been carried out for a variety of assumptions concerning heat-transfer to and heat rejection from, the cryostat. It is shown that, even when unrealistically conservative assumptions are made in illustrative calculations, the temperatures do not approach melting point for any part of the plant structure. In all cases, maximum temperatures are reached within 1 year. It is also concluded that for the baseline scenario for ITER-FEAT in which helium gas is assumed to be present in the cryostat, convectively transferring heat between components, the outboard first-wall temperature never exceeds 530°C. A significant improvement could still be made if the surface emissivity of the thermal shields could be increased by some means during the post-accident period. © 2001 Published by Elsevier Science B.V. Keywords: ITER; Accidents; Design concepts
1. Introduction As part of the assessment of the safety performance of two design concepts for a burning plasma experiment, we describe bounding calculations of temperature transients for a hypothetical beyonddesign-basis (Category V) type accident in the proposed EU-I and International Thermonuclear Experimental Reactor-Fusion Energy Advanced Tokamak (ITER-FEAT) designs. These designs have evolved since the first Engineering Design Activities (EDA) phase of ITER concluded in July 1998, with its final design report (FDR) specifying E-mail address: [email protected] (W.E. Han).
a device, which is now known as ITER-FDR. Following that phase, there was an immediate exploration of options for a smaller alternative, which would involve reduced costs and also meet reduced technical objectives. A range of alternatives were defined, following which two further concepts (EU-I and ITER-FEAT) were further developed. The main parameters of these two concepts are compared with Table 1. They are broadly similar but further developments are likely to be based on ITER-FEAT. The hypothetical accident scenario is a complete loss of all active cooling from all systems for an indefinite period of time, as a bounding case. The calculations of resulting temperature transients are performed using CULTRAN [1], a code
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which models the radial heat-transfer in the structure of a fusion power plant in 1-D cylindrical geometry, based on dimensions applying to the radial build at the toroidal midplane. In this model, the main components are represented as homogeneous cylindrical layers. Although this approach does not take into account the toroidal spacing between individual toroidal field coils, the resulting simplification has a conservative impact on the temperature transient calculations. Each cylindrical layer may either be in thermal contact with a neighbouring one or separated from it by a gap. If there is a gap, heat-transfer across the gap may occur either through radiation or through use of a heat-transfer coefficient, in proportion to the temperature difference between the two surfaces. The only heat source assumed to drive the temperature excursions is the decay-heat of plant structures. This decay-heat data was obtained from calculations which assumed that all components had received the maximum possible operational irradiation history, which covers a period of about 10 years. The divertor was not modelled, although CULTRAN has the capability to do this when data is available for this component. 2. EU-I calculations The EU-I radial build specified by Daenner [2] was used in the CULTRAN model. Some of the scenario variations analysed in the thermal transient calculations relate to the outermost component included in the model, which is the cryostat comprising a concrete bioshield with internal steel liner. A gap between the liner and the concrete allows for the potential of a cooling flow of air, driven by natural convection, to remove heat from the liner. When this convective cooling is being modelled there is no need to take account of the concrete bioshield which is then omitted. If no convective cooling is assumed, then the less efficient alternative of conductive heat loss through the concrete bioshield is modelled. Some of the materials compositions for some EU-I components were provided by Cepraga [3], who also gave the decay-heat values used [4,5]. The crucial factors affecting post-accident temperature evolution are those relating to heat-
transfer between vacuum vessel and magnets, between magnets and cryostat, and heat removal from the cryostat. If there is no gas within the cryostat, then heat-transfer across any gaps must occur radiatively but, if gas (i.e. air or helium) is allowed in, then we need to account for the possibility of convective heat transfer. The convective case is dealt with by employing heat transfer coefficients of 1.3 and 2.3 Wm − 2 K − 1, depending on whether the gas is air or helium, respectively. These values were as used by Bartels in CHEMCON analyses [6], arising from assessments by Iseli [7] of thermal transport across thermal shields in ITER. Different cases were analysed to reflect different scenarios and to explore sensitivity to variations in assumptions made but, in view of the diminished interest in EU-I, we will look here at only two cases corresponding to the most benign and the most severe sets of assumptions for which the calculations were performed.
2.1. Helium in cryostat We take account of the effects of convective cryostat cooling, although neither the cryostat nor the bioshield are explicitly included in the calculation. This is accomplished by applying a heattransfer coefficient of 2 Wm − 2 K − 1, with respect to ambient temperature, to the outer surface of
Table 1 Comparison of main parameters of EU-I and ITER-FEAT concepts EU-I R (m) A (m) Ip (MA) B0 (T) Aspect ratio q95 Peak toroidal field (T) Toroidal field energy (GJ) Fusion power (MW) Mean neutron wall loading (MW m−2)
5.48 1.72 13.0 5.16 3.18 3.0 11.8 29 530 0.8
ITER-FEAT 6.20 2.0 15.0 5.3 3.10 3.0 11.8 41 500 0.57
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Fig. 1. Upper-bound temperature history, following loss of all cooling, in the outboard components of the EU-I model for the case of helium in the cryostat. The lower curve represents the magnets. Above this, the curves for fronts and backs of vacuum vessel, blanket and first-wall are also plotted and, after around 10 days, are seen to span a narrow range.
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bioshield was included, but there was no assumption of cooling flow behind the liner. Convective heat-transfer in air between vacuum vessel and magnets (heat-transfer coefficient of 1.3 Wm − 2 K − 1) was assumed. The magnet surface emissivity was taken to be 0.05 (based on safety and environmental assessment of fusion power (SEAFP) studies [8] in the absence of specific EU-I data), and heat-transfer between magnets and cryostat was by radiation. Although, this is not a fully consistent set of assumptions, the modelling of the heat-transfer between magnets and cryostat in this way was undertaken to add extra conservatism to the calculation. The results of this calculation appear in Fig. 2, showing the maximum first-wall temperature of about 630°C being attained at around 1 year.
3. ITER-FEAT calculations the magnets in the CULTRAN model. It was confirmed through auxiliary calculations that this gave a reasonable simulation of what would happen if the cryostat steel liner had been included and there had been a cooling flow of air due to natural convection at its outer surface, removing heat at the rate of 4 Wm − 2 K − 1. The prescribed heat-transfer coefficient of 2.3 Wm − 2 K − 1 was used to model convective heat-transfer in helium between vacuum vessel and magnets. The temperature histories, obtained from the CULTRAN calculations, of the outboard components appear in Fig. 1. The uppermost curve represents the first-wall temperature and it can be seen that at the end of the calculation (about 83 days), the first wall temperature is about 330°C. Note that temperatures are still rising gently at this point in time.
The source of the design data is reference [9]. As prescribed in this document, a safety factor of 1.2 was applied to the decay-heat values given.
2.2. No cooling flow inside liner
Fig. 2. Upper-bound temperature history, following loss of all cooling, in the outboard components of the EU-I model for the case of no convective cooling of the cryostat liner. At the end of the calculation, the component temperature histories appear in the following temperature order (starting with the lowest temperature); (1) Back of bioshield; (2) cryostat and front of bioshield, (3) magnets. Above these, the temperatures of fronts and backs of vacuum vessel, blanket and first-wall are also plotted, and are seen to span a narrow range.
This calculation (the worst case analysed) was performed to illustrate the consequences of an extreme set of assumptions and, in order to assess their potential severity, was continued until all components had reached their maximum temperature. For this scenario, the cryostat with concrete
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Again, a number of scenarios were analysed, and the presence of either helium or air in the cryostat was modelled with the same heat-transfer coefficients as those used in the EU-I calculations for heat-transfer to and from the magnets. In this design, there is a steel cryostat and concrete bioshield separated by a gap, allowing the potential for a similar cooling flow of air to that which might occur behind the cryostat liner in the EU-I design. To simulate this convective cooling of the cryostat, we follow the procedure used in reference [6] and apply the heat removal rate of 4 Wm − 2 K − 1 relative to ambient temperature (taken to be 300 K). Calculations were performed for four different scenarios. The first three included the convective heat removal from the outer surface of the steel cryostat and corresponded to the three cases of helium, air, or no gas within the cryostat. The fourth did not include the cooling of the cryostat with natural convection air flow and did not assume the presence of gas in the cryostat. This is the order in which the results are presented.
3.1. Helium in cryostat We apply the convective heat removal rate of 4 Wm − 2 K − 1 to the outer surface of the cryostat. Thus, we do not model the concrete bioshield. We assume a heat-transfer coefficient of 2.3 Wm − 2 K − 1 between vacuum vessel and magnets, and between magnets and cryostat. The calculated temperature histories of outboard components for this case are shown in Fig. 3. It can be seen that the peak first-wall temperature is about 530°C, occurring after around 8 months. Inspection of those curves also reveals that the main barriers to heat rejection are the thermal shields and cryostat heat removal rate.
3.2. Air in cryostat Again the concrete bioshield is not modelled and, instead, we apply heat removal at the rate of 4 Wm − 2 K − 1 at the outer surface of the cryostat. This time we assume a heat-transfer coefficient of 1.3 Wm − 2 K − 1 between vacuum vessel and magnets, and between magnets and cryostat.
Fig. 3. Upper-bound temperature history, following loss of all cooling, in the outboard components of the ITER-FEAT model for the case of helium in the cryostat. At the end of the calculation, the component temperature histories appear in the following temperature order: (1) cryostat 122°C, (2) back of magnets 287°C, (3) front of magnets 308°C. Above these, the temperatures of fronts and backs of vacuum vessel, blanket and first-wall are also plotted, and are seen to span a narrow range.
The results can be inspected in Fig. 4, which shows that the behaviour is similar to the helium case and, again, the main barriers to heat rejection are the thermal shields and cryostat heat removal rate. However, maximum temperatures are a little higher, with the first-wall peaking at about 675°C in around 11 months.
3.3. No gas in cryostat This is the third scenario in which the concrete bioshield is not modelled and in which we apply heat removal at the rate of 4 Wm − 2 K − 1 at the outer surface of the cryostat. However, as there is assumed to be no gas within the cryostat, heattransfer between vacuum vessel and magnets is via radiation through the thermal shield, modelled as a single layer, with emissivity on both surfaces assumed to be 0.03. This is based on information given in reference [9]. The thermal shield between magnets and cryostat is also modelled with these properties. The results of these calculations appear in Fig. 5, which shows that the in-vessel components become hotter than in the earlier calculations,
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with the first-wall peak temperature of around 730°C occurring in around 9 months. It can be seen that the thermal shields are now even more of a barrier to heat rejection as there is no convectively aided heat-transfer within the cryostat in this scenario. However, it can also be seen that the cryostat remains relatively cool. Hence, we may conclude that the value of the heat removal rate assumed from this component is of lesser importance, when there is no gas in the cryostat.
3.4. No cryostat con6ecti6e heat remo6al This is the worst case. This is similar to the earlier case in that there is assumed to be no gas within the cryostat. Hence, heat-transfer to and from the magnets is, again, through the thermal shields via radiation at the surfaces, with emissivity on both surfaces of each shield assumed to be 0.03. However, the concrete bioshield is modelled this time and the cryostat can now only lose heat by radiating to the inner surface of the concrete, which is a poor conductor. Note that inclusion of the bioshield accentuates the inability of cylindrical geometry to accurately represent the three-di-
Fig. 4. Upper-bound temperature history, following loss of all cooling, in the outboard components of the ITER-FEAT model for the case of air in the cryostat. At the end of the calculation, the component temperature histories appear in the following temperature order: (1) cryostat 111°C, (2) back of magnets 367°C, (3) front of magnets 384°C. Above these, the temperatures of fronts and backs of vacuum vessel, blanket and first-wall are also plotted, and are seen to span a narrow range.
Fig. 5. Upper-bound temperature history, following loss of all cooling, in the outboard components of the ITER-FEAT model for the case of no gas in the cryostat. At the end of the calculation, the component temperature histories appear in the following temperature order: (1) cryostat 102°C, (2) back of magnets 404°C, (3) front of magnets 523°C, (4) front of magnets 537°C, (5) thermal shield 624°C. Above these, the temperatures of fronts and backs of vacuum vessel, blanket and first-wall are also plotted, and are seen to span a narrow range.
mensional nature of the problem. The effect of this is to introduce even more conservatism into the results. It is evident from the temperature histories, shown in Fig. 6, that the first-wall, peaking at around 745°C in around 10 months, is only hotter by about 15°C compared with the earlier case with convective cryostat cooling. This is a very modest increase, despite the fact that the cryostat maximum is now around 140°C hotter. It would seem that, when there is no gas in the cryostat, the temperature histories of the in-vessel components are not greatly dependent on the variations we have explored concerning details of the cryostat/bioshield heat-rejection. Whether or not cryostat convective cooling is assumed, the cryostat temperature adjusts to that required to achieve matching of total decay-heat production and heat-rejection when component temperatures are reaching a plateau at around 10 months. Thus, although there is a large temperature drop across the bioshield, this does not allow us to conclude that it is a significant heat barrier in this particular case. Comparison with the earlier sce-
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nario indicates that even if the cryostat were maintained at ambient temperature it could not significantly alter the behaviour of the first-wall temperature as it is actually the thermal shields which are the main barriers to heat removal if there is no gas in the cryostat.
4. Discussion and conclusions EU-I and ITER-FEAT results are broadly similar and do not appear to be sensitive to factors relating to heat-transfer in first-wall and blanket regions. The presence of helium in the cryostat gives the best conditions for heat removal but, even with this benefit, estimates based on these calculations suggest that heat removal could be significantly enhanced and substantial reductions in maximum temperatures achieved, if surface emissivities of the thermal shields were to greatly exceed 0.05. Unfortunately, the aim of designing effective thermal shielding conflicts with the need for heat rejection in the event of a hypothetical loss of coolant. However, dramatic improvements
might be achieved using designs which degrade, following moderate temperature excursions, to give higher emissivity characteristics. Such a shield design has been assumed in SEAFP studies [8]. There the thermal shield was constructed from multiple layers of metalised plastic foil needing only a modest temperature rise in order to melt. It has been established that, even when making the most extreme assumptions, the maximum outboard first-wall temperature of around 745°C occurs at about 1 year after the loss of coolant. Thus, for all cases considered, temperatures remain far below melting point for any of the plant structures. Furthermore, the scenarios which do not include gas in the cryostat should be viewed as highly unrealistic since continuous pumping effort is required to exclude the air. The worst case calculations should therefore be viewed as illustrative only. In the case of ITER-FEAT, the presence of helium, as opposed to air, in the cryostat lowers maximum temperature by around 145°C and it is reasonable to assume that this would be introduced into the cryostat to reduce the accident consequences, by operator action, within the first day. This should be regarded as the base case scenario. More accurate calculations will be possible with a three-dimensional model of the designs. Work is under way to do this at Culham. Computational fluid dynamics will also allow the heat-transfer associated with natural convection flows within the plant to be simulated. Acknowledgements This work was funded by the UK Department of Trade and Industry and EURATOM.
Fig. 6. Upper-bound temperature history, following loss of all cooling, in the outboard components of the ITER-FEAT model for the case of no gas in the cryostat and no cryostat convective cooling. At the end of the calculation, the component temperature histories appear in the following temperature order: (1) back of bioshield 27°C, (2) front of bioshield 209°C, (3) cryostat 253°C, (4) thermal shield 463°C, (5) back of magnets 547°C, (6) front of magnets 561°C, (7) thermal shield 641°C. Above these, the temperatures of fronts and backs of vacuum vessel, blanket and first-wall are also plotted, and are seen to span a narrow range.
References [1] W.E. Han, N.P. Taylor, Calculations of temperature and mobilisation evolution for postulated accidents in SEAFP plant models., in: Proceedings of the 18th Symposium on Fusion Technology, Karlsruhe, Germany, 22 – 26 August 1994, Elsevier, Amsterdam, 1995, p. 1493. [2] W. Daenner, EU-I Radial Build Level 2, note forwarded by W. Gulden on 20 April 1999.
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D. Cepraga, private communication, 7 May 1999. D. Cepraga, private communication, 18 May 1999. D. Cepraga, private communication, 15 September 1999. H.-W. Bartels, Preliminary assessment of decay-heat in RC-ITER, ITER internal report, S81 RI 28 98-10-08, version 4, 12 February 1999. [7] M. Iseli, Heat transfer between VV, thermal shield and magnets with air or helium atmosphere in the cryostat, N
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80 MD 2 96-09-19, ITER NAKA JWS, September 1996. [8] N.P. Taylor, I. Cook, C.B.A. Forty, W.E. Han, P. Taylor, SEAFP-2 bounding accident analyses, Proceedings of the sixth IAEA Technical Committee Meeting on Fusion Power Plant Design, 23 – 27 March, Culham, Oxfordshire, 1998. [9] H.-W. Bartels, L. Topilski. (Eds.), Safety Analysis Data List-3 (SADL-3), Version 1.0, 29 February 2000.