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Numerical simulation of the temperature response of the JET Bulk-W Divertor Row on pulsed heat loading
Fusion Engineering and Design 84 (2009) 853–858
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Numerical simulation of the temperature response of the JET Bulk-W Divertor Row on pulsed heat loading S. Grigoriev a,c , Ph. Mertens a,b , O. Neubauer a,b , S. Sadakov a,b , K. Senik a,c , V. Tanchuk a,c,∗ a b c
JET-EFDA, Culham Science Centre, OX14 3DB, Abingdon, UK Institute for Energy Research IEF-4 (Plasma Physics), Forschungszentrum Jülich, Association EURATOM-FZJ, Trilateral Euregio Cluster, D-52425 Jülich, Germany SINTEZ Scientific Technical Centre, D.V. Efremov Scientific Research Institute of Electrophysical Apparatus, RUS-196641 St. Petersburg, Russia
a r t i c l e
i n f o
Article history: Available online 9 January 2009 Keywords: JET divertor Load-bearing septum replacement plate (LB-SRP) CFC base plate (BP) Global wetted fraction (GWF) Local wetted fraction (LWF) Tungsten Solid-tungsten design Thermal response Cyclic heat loading
a b s t r a c t The simulation of the thermal response of the JET bulk tungsten divertor modules to real operational conditions demonstrates that the analyzed design provides more favourable conditions than before (≤600 ◦ C) for the temperature-vulnerable materials of the stack attachment (esp. Inconel spring discs), thereby increasing the attachment lifetime. The computation shows that the JET divertor unit can withstand up to five consecutive cycles, 10 s long, of an evenly distributed heat loading (averaged heat flux of ∼6.5 MW/m2 ) with half-an-hour intervals before the springs reach their uppermost temperature limit. However, if we take into account: (i) the real heat load distribution over the upper lamellae surface (shadowing effect), (ii) an initial temperature of the structure of 200C, it may be that the temperature approaches 600C after a single full-energy pulse. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The comprehensive thermal analysis of the “Wedge-7” design option [1] for the LB-SRP demonstrated, in general, the JET divertor capability to withstand averaged heat loads generated by the plasma without active cooling. At the same time, the obtained results raised the question as to the workability of (1) Inconel tie-rods fixing lamellae and spacers together in one rigid stack and (2) spring-washers used to produce pre-tension and to mitigate tierod tightness reduction due to its possible temperature elongation [2]. As calculated, the maximum temperature attained by tie-rods and spring-washers (1085 ◦ C and 1153 ◦ C, respectively) exceeds significantly the maximum operating temperature of 600 ◦ C specified for Inconel. There are doubts whether Inconel tie-rods and spring washers are capable of maintaining their elastic properties at such high temperatures. As a result, the lamellae attachment unit was modified: tie-rods were replaced by “chain type” attachments located in racetrackshaped central cutouts of lamellae and spacers [3]. Such a design of
∗ Corresponding author at: 3 Doroga na Metallostroy, p. Metallostroy, 196641 St. Petersburg, Russia. Tel.: +7 812 462 7836; fax: +7 812 464 4623. E-mail address: [email protected] (V. Tanchuk). URLs: http://www.niiefa.spb.su (S. Grigoriev), http://www.fz-juelich.de/ief/ief4 (Ph. Mertens). 0920-3796/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2008.11.057
the stacks attachment allows to move the temperature-vulnerable spring elements farther from the high temperature zone. The chain is made of Densamet® material [4] which extends its functionality to higher temperatures (700–1000 ◦ C). In order to evaluate how the proposed design improvements will impact the thermal performance of the JET divertor, cyclic thermal analyses of the FE model under averaged (qav = 6.43 MW/m2 on the actual tungsten surface) and realistic (GWF & LWF are taken into account) heat loading conditions were performed. The paper reports the results of the thermal analysis performed. 2. Description of the design The solid-tungsten design option for the LB-SRP in the JET divertor has gone through a series of modifications described in detail in Refs. [2,5,6]. The current design option of the JET divertor unit (Fig. 1) exploits a chain for attachment of plasma-facing components to the supporting structure. For this purpose, the wedge and lamellae design were slightly modified so as to use a clamping chain in the divertor design. The chain performs two functions: (1) maintaining the stack rigidity or structural integrity and (2) pulling the stack onto the carrier (a wedge with eight “wings”). The chain has four, partially redundant rows of Densamet links with pins made of Nimonic® alloy. The actual fixings consist in six anchor bolts made of Nimonic. They carry the spring elements, which are thus located below the
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Fig. 1. General view of the JET divertor unit (near-final design option).
wing, away from the hottest parts. They are compressed against a Densamet rail, which is trapped inside the channel of the wing. Ceramic-coated foils are located on the “shoulders” of the wings to ensure sliding and more uniform structural and thermal contact. 3. Development of 3D FE model for thermal analysis A full-scale model of the JET divertor unit reflects the real divertor (a) configuration, (b) composition, (c) materials and is close to the real geometry. Only minor geometric simplifications were used. Contact layers 0.25 mm in thickness incorporated in some places of the model slightly increase the dimensions. It should be noted that neither these simplifications nor contact layers do affect noticeably the thermal behaviour of the model. The FE model consists of four main parts: (1) eight plasma-facing tiles comprising 24 tungsten lamellae and 23 TZM spacers; (2) one supporting structure or Inconel® wedge; (3) one Inconel adaptor plate serving to bring the modified supporting structure into coincidence with the unchanged base plate and (4) CFC base plate resting on the water-cooled Inconel supporting plate. Different attachment units (chains, anchors, bolts, nuts and washers) are modelled to provide the divertor rigidity and model correct behaviour under the specified loads. Contact layers are included in the FE model to simulate deterioration of heat exchange between the elements composing the divertor unit due to insulating coatings (Al2 O3 or ZrO2 ) or thermal contact imperfectness.
The data available from literature [7] make it possible to summarize that beryllium emissivity strongly depends on the surface conditions (oxide level, roughness) and increases with the surface temperature (from ∼0.3 up to ∼0.5–0.6). Assuming that (1) the JET First Wall (FW) temperature during operation is constant and equals 200 ◦ C; (2) the beryllium surface degrades with the number of cycles and (3) part of the FW is coated with other materials, an averaged value of εBe = 0.5 was proposed for the thermal analysis. The CFC emissivity of εCFC = 1.0 was used in our analysis to describe heat exchange by radiation between the lower wedge surface and CFC base plate carrying the divertor unit. Assuming that the wedge surface facing the base plate (1) did not undergo any polishing treatment in order to reduce its emissivity and (2) is subject to possible carbon deposition caused by chemical sputtering of the base plate surface, the Inconel emissivity εinc = 0.5 is taken for the thermal analysis. The effective emissivities between the tungsten lamellae and the beryllium FW and between the inconel wedge and CFC base plate were evaluated to εeff.1 = 0.25 and εeff.2 = 0.5, respectively. These values were used in the thermal analysis performed. 3.2. Contact layers Special attention was paid to the contact layers between different components of the JET divertor unit used to model thermal resistance in the interface areas. The following contacting areas were identified: three interfaces between the lamellae and coated wedge (ZrO2 ), between the lamellae and oxide (Al2 O3 ) coated and non-coated spacers, one interface between the adaptor and wedge (through the bolts and pins), an interface between the adaptor and base plate (two contacting areas), interfaces between the chain, ZrO2 inserts and spacers and, finally, an interface between the wedge supports and CFC base plate. A thickness of 0.25 mm was chosen for all contact layers. It is assumed that the thermal conduction of the areas simulating the oxide coating and the imperfect thermal contact take into account of Al2 O3 (lamella/spacer) or ZrO2 (lamella/wedge) conductivities. The conductivity of the contact layer representing only the imperfect thermal contact (lamella/non-coated spacer and copper-coated wedge support/CFC base plate) is assumed to be as high as 50% of the TZM and 66% of the Inconel conductivities, respectively. 4. Task formulation and loading conditions The calculation scheme presented in Fig. 2 was used in the thermal analysis to describe the transient behaviour of the JET divertor unit under the cyclic heat load.
3.1. Materials emissivity The results obtained in Ref. [1] reveal that radiation is the decisive mechanism responsible for the divertor cooling. That is the reason why the emissivity of the surface involved in the heat exchange process during cool-down plays a crucial role and shall be carefully defined in the thermal analyses. One can find below the guideline used for selection of one or another value for the emissivity. Tungsten emissivity depends essentially on the temperature of the radiating surface. The ITER Material Properties Handbook [7] indicates that the emissivity of pure tungsten will change from 0.032 up to 0.296 with the surface temperature increasing from 300 K to 2400 K. Moreover, as noted in the document, surface finishing and oxides can significantly alter (increase) the emissivity of metal. For thick plates (>6 mm) the ITER MPH recommends using the emissivity of ε = 0.39, typical for low dense tungsten. As a compromise, a mean value (between 0.296 and 0.39) of εw = 0.34 was used for the thermal analysis of the JET tile behaviour.
Fig. 2. Calculation scheme of the JET divertor unit for thermal analysis.
S. Grigoriev et al. / Fusion Engineering and Design 84 (2009) 853–858
The heat flux qmax loads the lamellae surface during 10 s. This heat is absorbed by tiles and is accumulated inside the structure. A fraction of heat irradiates to the surface of the First Wall (εeff.1 = 0.25) surrounding the divertor. It is assumed that their temperature is 200 ◦ C and is time-constant. The heat absorbed by the tiles passes directly through the lamella body to the Inconel wedge through the ceramic strips located on the wings shoulders and via the spacers, heating meanwhile (1) the chain by conduction through the ZrO2 inserts and via chain closures from side lamellae, (2) the adaptor by conduction through the bolts between the adaptor and wedge. Then, the heat from the wedge and adaptor leaks to the cooled CFC base plate by radiation (εeff.2 = 0.5) and by conduction via the Inconel feet. Finally, the heat accumulated in the CFC base plate leaves its structure to the supporting plate via the toroidal strip contacts by conductance. The discussed physical model of the thermal process could be described by a well-known equation for the 3D transient non-linear heat conduction problem with the following boundary conditions: ∂t(x, y, z) = qabsorb − qrad ∂n
− for the lamellae upper surface (4.1)
∂t(x, y, z) =0 ∂n
∂t(x, y, z) = −qrad ∂n
t(x, y, z)
base/ sup
− for the divertor lateral surfaces − for the lower wedge surface
= T0
(4.2) (4.3)
− for the CFC BP/supporting plate
contact area
(4.4)
Fig. 3. Heat loading scheme in the JET machine for the cyclic analysis.
This heat load of 5.0 MW/m2 for the spatial conical surface can be recalculated for the total area of upper metallic surfaces of lamellae, including all shadowed and wetted areas on the top surfaces (this is how the load is applied to the FE model). This re-calculation yields a heat load of 6.43 MW/m2 × 10 s for metal. The pulse repetition time is 1800 s. So, for the cyclic analysis under the averaged uniform heat loading it is assumed that during 10 s the upper surfaces of the divertor tiles are loaded with a uniform heat flux of 6.43 MW/m2 . And during a pause of 1790 s the divertor is cooled down passively by (a) radiation to the FW (εeff.1 = 0.25) and base plate (εeff.2 = 0.5) and (b) conduction to the base plate/supporting plate contact area.The cyclic loading reflecting the time needed to gain quasi-steady-state conditions (5 pulses) can be written as:
Here:
- t(x,y,z)|=0 = T0 is the divertor initial temperature; 4 ) is the heat flux lost to the in- qrad = εeff ϕ(T 4 (x, y, z) − Tsurroundings
vessel components by radiation, where = 5.67 × 10−8 W/m2 K4 ; - T(x,y,z) = t(x,y,z)ext surf is the divertor external surface temperature; is the effective emissivity defined as - εeff εeff = 1/(1/εtile + 1/εsurroundings − 1); - ϕ = 1 is the geometric configuration factor between the divertor surface and the surfaces of the in-vessel components.
Tsurroundings =
200◦ C, for the upper surface; Tbase plate, for the lower surface;
T0 = 35 ◦ C; qabsorb () = 6.43 MW/m2 ×
1, for ∈ pulse 0, for ∈ pause.
855
2
qload = 6.43 MW/m ×
1, 0,
1800n ≤ ≤ 1800n + 10 , 1800n + 10 < < 1800(n + 1)
where n = 0–5 is the number of pulses.
4.2. Realistic heat loading Fig. 4 describes of input thermal loads used to analyze thermal transients in the divertor structure taking into account the global and local shadowing effect (cf. [8]). The discussed input loads are consistent with those described in the previous section, but, of course, specific power density for the lamellae exposed to the heat loads is higher than an average power for all lamellae, since some other lamellae are unloaded due to stack-to-stack shadowing effects and other reasons.
4.1. Loading conditions The current analysis is performed for the static configuration of heat loads. This means that no sweeping effects (double exposition at the edges, different repetition time for the tile centre and tile edges, etc.) have been analyzed. An input load for the thermal analysis (surface density of the thermal power and energy) is specified as 5.0 MW/m2 × 10 s, where the area is the entire conical surface (frustum) covering the divertor row, including all gaps and top surfaces of all lamellae with all wetted and shadowed areas (see Fig. 3). JET originally specified this value as independent of the field angle and constant with the radial coordinate.
Fig. 4. Shadowing effect for lamellae nominal position.
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Fig. 7. Evolution of the maximal temperature of the JET divertor. Fig. 5. FE global model of the JET divertor. Mesh.
The cyclic analysis under the averaged heat loading makes it possible to determine, first, the number of machine operational cycles to attain the quasi-steady-state conditions of the divertor temperatures and, second, the maximal temperatures attainable by different divertor components: lamella, wedge, chain, adaptor and base plate in order to confirm their workability as it is or to outline the range of acceptable operational conditions.
Fig. 7 illustrates the JET divertor temperature response (lamella maximal temperature) to the cyclic loading conditions. One can see from the temperature curve shown in this figure that the quasisteady-state conditions are gained in five cycles. Hand in hand with the reaching a quasi-steady-state condition with the number of pulses (1) the divertor maximal temperature increases from 1387 ◦ C up to 1915 ◦ C (Fig. 8) and (2) the divertor residual temperature will also increase from 374 ◦ C to 615 ◦ C. The wedge temperature spatial distribution shown in Fig. 9 demonstrates evidently that the wedge area contacting the lamellae “legs”, even though protected with thermal insulating (ZrO2 ) strips, attains ∼1055 ◦ C. The wedge reaches its maximal temperature 40 s after the beginning of exposure to the specified plasma, for each pulse. The area with the highest chain temperature is represented by the chain plugs, in contact with the side lamellae. A maximum temperature of 696 ◦ C is attained at the end of the pulse, i.e. in 10 s. The maximum temperature of the chain–rail assembly shifts with time from the plugs down to the anchors, where it reaches 234 ◦ C at the end of the first cycle. Starting from the second cycle, temperature states of the chain assembly are different for the upper and lower stacks due to nonequality of their residual temperatures before the second pulse. The chain temperature difference is as high as ∼330 ◦ C at the fifth operational cycle. If the most part of the chain structure attains a temperature of 1000–1100 ◦ C in 40 s of the last cycle, the temperaturevulnerable spring elements will not exceed 620 ◦ C during, at least, the first five pulses of the machine operation (Fig. 10). Note that a
Fig. 6. FE model of the wedge and adaptor. Mesh.
Fig. 8. Temperature state of the JET divertor assembly at the end of fifth pulse: = 7210 s; max temp: 1915 ◦ C.
5. Description of the ANSYS model The 3D FE ANSYS model [9] of the JET divertor unit (Figs. 5 and 6) was developed to simulate the divertor temperature response to the pulsed surface heat load. The model consists of 455 091 elements. A thermal mass solid, an 8-node brick, SOLID70 is the basic type of model elements applied for the transient thermal analysis. Together with the basic SOLID70, the thermal element SHELLl57, SURF152 and superelement MATRIX50 were used to build-up the 3D ANSYS model of different elements composing the JET divertor unit and to simulate the heat exchange process by radiation. 6. Calculation results and discussions 6.1. Cyclic analysis under the averaged heat loading of 6.43 MW/m2
S. Grigoriev et al. / Fusion Engineering and Design 84 (2009) 853–858
857
Table 2 Heat loading options.
Fig. 9. Temperature state of the divertor carrier (wedge) in 40 s after plasma start-up (fifth pulse): = 7240 s; max temp: 1055 ◦ C.
Lamellae position Field angle
Nominal, full power
1◦ 4◦
LWF = 0.60, Plocal = 26.8 MW/m2 LWF = 0.77, Plocal = 11.9 MW/m2
increase of its heat flux values. To evaluate the influence of the “shadowing” effect the real loading conditions taking into account the lamella wetted fraction are simulated according to the calculation scheme shown in Fig. 4. Table 2 summarizes all calculation options analyzed in the performed study. The obtained results are shown in Figs. 11 and 12 and in Table 3. Here, one can find the pictures demonstrating the influence of the “shadowing effect” on (1) the JET divertor, (2) wedge and (3) chain assembly temperature states. It is clear from Fig. 11 that the lamellae could survive only 7.25 s of the heat load determined for the nominal lamella position and a field angle of 1◦ (q1◦ = 26.788 MW/m2 ). Just after 6 s of the plasma burning start-up the lamellae surface attains a tungsten melting temperature of ∼3400 ◦ C. A heat loading angle of 4◦ (q4◦ = 11.927 MW/m2 ) allows for the lamella to withstand a straight loading cycle of 10 s for the whole range of the specified power for the nominal lamella position (Fig. 12).
Fig. 10. Temperature state of chain assembly at the end of fifth cycle. (Stack 1. = 9000 s. Max temp: 615 ◦ C).
more sensible temperature limit for the spring elements amounts to 500 ◦ C, which reduces the number of such pulses to about 2, depending on the inter-shot cooling time. The temperature of the chain side covers (1280 ◦ C) approaches the Nimonic melting point of 1345 ◦ C at the end of the fifth pulse (7210 s). The thermal analysis showed that 2 mm ceramic washers placed below the oval cover plates make it possible to reduce the maximal temperature attainable by the chain covers from 1280 ◦ C down to ∼1060 ◦ C. Table 1 gives the maximal temperatures gained by different components of the JET divertor unit during the cyclic operation at the averaged heat loading q = 6.43 MW/m2 . 6.2. Cyclic analysis under the realistic heat loading (GWF&LWF) The “shadowing” effect (Fig. 4) causes a non-uniform heat load distribution over the lamellae upper surface and a subsequent Table 1 Summary of peak temperatures (◦ C) for divertor components. No.
1. 2. 3. 4. 5.
Component
Lamella Wedge Adaptor Chain Base plate
Heat flux = 6.43 MW/m2 First pulse
Last pulse
1387 613 166 696 54
1915 1055 312 1280 67
Fig. 11. JET divertor (a) and wedge (b) temperature state at ϑ = 1◦ , GWF = 0.4 & LWF = 0.6, =8 s: lamella − Tl.max = 3441 ◦ C; (b) wedge − Tw.max = 476 ◦ C.
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S. Grigoriev et al. / Fusion Engineering and Design 84 (2009) 853–858 Table 3 Summary of the thermal analysis.
Lamella ϑ = 90◦ ϑ = 4◦ ϑ = 1◦ Wedge ϑ = 90◦ ϑ = 4◦ ϑ = 1◦
GWF
LWF
Heat (MW/m2 )
Time (s)
Max temp (◦ C)
1 0.7 0.7 0.4 0.4
1 1 0.77 1 0.6
6.43 9.18 11.9 16.07 26.79
10 10 10 10 8
1387 1959 2228 3164 3440
1 0.7 0.7 0.4 0.4
1 1 0.77 1 0.6
6.4 9.18 11.9 16.07 26.79
40 40 40 40 8
615 831 830 1281 476
from ∼7.25 s to 2.75 s (for a field angle of 1◦ , full power heat and the lamella nominal position). 7. Conclusions The thermal analysis in support of the JET divertor unit makes possible the following conclusions. The current design of the JET divertor unit provides more favourable operation conditions for the temperature-vulnerable materials of the stack attachment thereby increasing the attachment lifetime. Thus, the model simulation performed shows that the JET divertor unit is capable to withstand a couple of full-energy cycles with an averaged heat flux of 6.43 MW/m2 following at a 30min repetition time. Up to five cycles indeed if we would consider the melting points as being the limit (a reserve factor has obviously to be specified). However, if we take into account (i) the real heat load distribution over the upper lamellae surface (shadowing effect even at the lamellae nominal, i.e. non-elevated position); (ii) an initial temperature of the divertor structure of 200 ◦ C (instead of 35 ◦ C) after the baking procedure; (iii) possible uncertainties as to the material properties and calculation accuracy, it may be that the temperature approaches 600 ◦ C after a single full-energy pulse. Acknowledgements This work, supported by the European Communities under contracts between EURATOM and Forschungszentrum Jülich, was carried out within the framework of the European Fusion Development Agreement (EFDA). The views and opinions expressed herein do not necessarily reflect those of the European Commission. References
Fig. 12. JET divertor and its components temperature state at ϑ = 4◦ , GWF = 0.7 & LWF = 0.77, = 10 s: lamella − Tl.max = 2228 ◦ C; (b) wedge − Tw.max = 830 ◦ C; (c) chain − Tc.max = 825 ◦ C.
It should be noted that the results presented in Figs. 11 and 12 reflect the influence of the heat loads “shadowing” on the JET divertor temperature state in case of heat loading onto the “cold” divertor unit (the divertor initial temperature before heat loading equals to 35 ◦ C). For quasi-steady state conditions (the divertor residual temperature is ∼600–700 ◦ C), the lamella lifetime (an operation time to attain the tungsten melting temperature) is reduced significantly:
[1] Thermal analysis of the JET LB-SRP divertor, Final Report, January 2007 (Internal JET-EFDA document). [2] Ph. Mertens, T. Hirai, J. Linke, O. Neubauer, G. Pintsuk, V. Philipps, S. Sadakov, U. Samm, B. Schweer, Fusion Eng. Des. 82 (2007) 1833–1838. [3] Ph. Mertens, H. Altmann, T. Hirai, M. Knaup, O. Neubauer, V. Philipps, J. Rapp, V. Riccardo, S. Sadakov, B. Schweer, A. Terra, I. Uytdenhouwen, U. Samm, Fusion Eng. Des, doi:10.1016/j.fusengdes.2008.11.055, submitted for publication. [4] Densamet is a registered trademark of MG Sanders Ltd., Stone, U.K. [5] Ph. Mertens, JET W-bulk Team, in: T. Hirai, Ph. Mertens (Eds.), Conceptual design for a tungsten bulk LB-SRP, Final Report, March 2006 (internal JET-EFDA document). [6] T. Hirai, H. Maier, M. Rubel, Ph. Mertens, R. Neu, O. Neubauer, et al., R&D on full tungsten divertor and beryllium wall for the JET ITER-like Wall Project, Fusion Eng. Des. 82 (2007) 1839–1845, doi:10.1016/j/fusengdes.2007.02.024. [7] ITER Material Properties Handbook, ITER Document No. S74 RE 1. [8] J. Rapp, G. Pintsuk, Ph. Mertens (on Power Handling of the LBSRP), in press. [9] ANSYS Release 10.0.
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Numerical simulation of the temperature response of the JET Bulk-W Divertor Row on pulsed heat loading S. Grigoriev a,c , Ph. Mertens a,b , O. Neubauer a,b , S. Sadakov a,b , K. Senik a,c , V. Tanchuk a,c,∗ a b c
JET-EFDA, Culham Science Centre, OX14 3DB, Abingdon, UK Institute for Energy Research IEF-4 (Plasma Physics), Forschungszentrum Jülich, Association EURATOM-FZJ, Trilateral Euregio Cluster, D-52425 Jülich, Germany SINTEZ Scientific Technical Centre, D.V. Efremov Scientific Research Institute of Electrophysical Apparatus, RUS-196641 St. Petersburg, Russia
a r t i c l e
i n f o
Article history: Available online 9 January 2009 Keywords: JET divertor Load-bearing septum replacement plate (LB-SRP) CFC base plate (BP) Global wetted fraction (GWF) Local wetted fraction (LWF) Tungsten Solid-tungsten design Thermal response Cyclic heat loading
a b s t r a c t The simulation of the thermal response of the JET bulk tungsten divertor modules to real operational conditions demonstrates that the analyzed design provides more favourable conditions than before (≤600 ◦ C) for the temperature-vulnerable materials of the stack attachment (esp. Inconel spring discs), thereby increasing the attachment lifetime. The computation shows that the JET divertor unit can withstand up to five consecutive cycles, 10 s long, of an evenly distributed heat loading (averaged heat flux of ∼6.5 MW/m2 ) with half-an-hour intervals before the springs reach their uppermost temperature limit. However, if we take into account: (i) the real heat load distribution over the upper lamellae surface (shadowing effect), (ii) an initial temperature of the structure of 200C, it may be that the temperature approaches 600C after a single full-energy pulse. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The comprehensive thermal analysis of the “Wedge-7” design option [1] for the LB-SRP demonstrated, in general, the JET divertor capability to withstand averaged heat loads generated by the plasma without active cooling. At the same time, the obtained results raised the question as to the workability of (1) Inconel tie-rods fixing lamellae and spacers together in one rigid stack and (2) spring-washers used to produce pre-tension and to mitigate tierod tightness reduction due to its possible temperature elongation [2]. As calculated, the maximum temperature attained by tie-rods and spring-washers (1085 ◦ C and 1153 ◦ C, respectively) exceeds significantly the maximum operating temperature of 600 ◦ C specified for Inconel. There are doubts whether Inconel tie-rods and spring washers are capable of maintaining their elastic properties at such high temperatures. As a result, the lamellae attachment unit was modified: tie-rods were replaced by “chain type” attachments located in racetrackshaped central cutouts of lamellae and spacers [3]. Such a design of
∗ Corresponding author at: 3 Doroga na Metallostroy, p. Metallostroy, 196641 St. Petersburg, Russia. Tel.: +7 812 462 7836; fax: +7 812 464 4623. E-mail address: [email protected] (V. Tanchuk). URLs: http://www.niiefa.spb.su (S. Grigoriev), http://www.fz-juelich.de/ief/ief4 (Ph. Mertens). 0920-3796/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2008.11.057
the stacks attachment allows to move the temperature-vulnerable spring elements farther from the high temperature zone. The chain is made of Densamet® material [4] which extends its functionality to higher temperatures (700–1000 ◦ C). In order to evaluate how the proposed design improvements will impact the thermal performance of the JET divertor, cyclic thermal analyses of the FE model under averaged (qav = 6.43 MW/m2 on the actual tungsten surface) and realistic (GWF & LWF are taken into account) heat loading conditions were performed. The paper reports the results of the thermal analysis performed. 2. Description of the design The solid-tungsten design option for the LB-SRP in the JET divertor has gone through a series of modifications described in detail in Refs. [2,5,6]. The current design option of the JET divertor unit (Fig. 1) exploits a chain for attachment of plasma-facing components to the supporting structure. For this purpose, the wedge and lamellae design were slightly modified so as to use a clamping chain in the divertor design. The chain performs two functions: (1) maintaining the stack rigidity or structural integrity and (2) pulling the stack onto the carrier (a wedge with eight “wings”). The chain has four, partially redundant rows of Densamet links with pins made of Nimonic® alloy. The actual fixings consist in six anchor bolts made of Nimonic. They carry the spring elements, which are thus located below the
854
S. Grigoriev et al. / Fusion Engineering and Design 84 (2009) 853–858
Fig. 1. General view of the JET divertor unit (near-final design option).
wing, away from the hottest parts. They are compressed against a Densamet rail, which is trapped inside the channel of the wing. Ceramic-coated foils are located on the “shoulders” of the wings to ensure sliding and more uniform structural and thermal contact. 3. Development of 3D FE model for thermal analysis A full-scale model of the JET divertor unit reflects the real divertor (a) configuration, (b) composition, (c) materials and is close to the real geometry. Only minor geometric simplifications were used. Contact layers 0.25 mm in thickness incorporated in some places of the model slightly increase the dimensions. It should be noted that neither these simplifications nor contact layers do affect noticeably the thermal behaviour of the model. The FE model consists of four main parts: (1) eight plasma-facing tiles comprising 24 tungsten lamellae and 23 TZM spacers; (2) one supporting structure or Inconel® wedge; (3) one Inconel adaptor plate serving to bring the modified supporting structure into coincidence with the unchanged base plate and (4) CFC base plate resting on the water-cooled Inconel supporting plate. Different attachment units (chains, anchors, bolts, nuts and washers) are modelled to provide the divertor rigidity and model correct behaviour under the specified loads. Contact layers are included in the FE model to simulate deterioration of heat exchange between the elements composing the divertor unit due to insulating coatings (Al2 O3 or ZrO2 ) or thermal contact imperfectness.
The data available from literature [7] make it possible to summarize that beryllium emissivity strongly depends on the surface conditions (oxide level, roughness) and increases with the surface temperature (from ∼0.3 up to ∼0.5–0.6). Assuming that (1) the JET First Wall (FW) temperature during operation is constant and equals 200 ◦ C; (2) the beryllium surface degrades with the number of cycles and (3) part of the FW is coated with other materials, an averaged value of εBe = 0.5 was proposed for the thermal analysis. The CFC emissivity of εCFC = 1.0 was used in our analysis to describe heat exchange by radiation between the lower wedge surface and CFC base plate carrying the divertor unit. Assuming that the wedge surface facing the base plate (1) did not undergo any polishing treatment in order to reduce its emissivity and (2) is subject to possible carbon deposition caused by chemical sputtering of the base plate surface, the Inconel emissivity εinc = 0.5 is taken for the thermal analysis. The effective emissivities between the tungsten lamellae and the beryllium FW and between the inconel wedge and CFC base plate were evaluated to εeff.1 = 0.25 and εeff.2 = 0.5, respectively. These values were used in the thermal analysis performed. 3.2. Contact layers Special attention was paid to the contact layers between different components of the JET divertor unit used to model thermal resistance in the interface areas. The following contacting areas were identified: three interfaces between the lamellae and coated wedge (ZrO2 ), between the lamellae and oxide (Al2 O3 ) coated and non-coated spacers, one interface between the adaptor and wedge (through the bolts and pins), an interface between the adaptor and base plate (two contacting areas), interfaces between the chain, ZrO2 inserts and spacers and, finally, an interface between the wedge supports and CFC base plate. A thickness of 0.25 mm was chosen for all contact layers. It is assumed that the thermal conduction of the areas simulating the oxide coating and the imperfect thermal contact take into account of Al2 O3 (lamella/spacer) or ZrO2 (lamella/wedge) conductivities. The conductivity of the contact layer representing only the imperfect thermal contact (lamella/non-coated spacer and copper-coated wedge support/CFC base plate) is assumed to be as high as 50% of the TZM and 66% of the Inconel conductivities, respectively. 4. Task formulation and loading conditions The calculation scheme presented in Fig. 2 was used in the thermal analysis to describe the transient behaviour of the JET divertor unit under the cyclic heat load.
3.1. Materials emissivity The results obtained in Ref. [1] reveal that radiation is the decisive mechanism responsible for the divertor cooling. That is the reason why the emissivity of the surface involved in the heat exchange process during cool-down plays a crucial role and shall be carefully defined in the thermal analyses. One can find below the guideline used for selection of one or another value for the emissivity. Tungsten emissivity depends essentially on the temperature of the radiating surface. The ITER Material Properties Handbook [7] indicates that the emissivity of pure tungsten will change from 0.032 up to 0.296 with the surface temperature increasing from 300 K to 2400 K. Moreover, as noted in the document, surface finishing and oxides can significantly alter (increase) the emissivity of metal. For thick plates (>6 mm) the ITER MPH recommends using the emissivity of ε = 0.39, typical for low dense tungsten. As a compromise, a mean value (between 0.296 and 0.39) of εw = 0.34 was used for the thermal analysis of the JET tile behaviour.
Fig. 2. Calculation scheme of the JET divertor unit for thermal analysis.
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The heat flux qmax loads the lamellae surface during 10 s. This heat is absorbed by tiles and is accumulated inside the structure. A fraction of heat irradiates to the surface of the First Wall (εeff.1 = 0.25) surrounding the divertor. It is assumed that their temperature is 200 ◦ C and is time-constant. The heat absorbed by the tiles passes directly through the lamella body to the Inconel wedge through the ceramic strips located on the wings shoulders and via the spacers, heating meanwhile (1) the chain by conduction through the ZrO2 inserts and via chain closures from side lamellae, (2) the adaptor by conduction through the bolts between the adaptor and wedge. Then, the heat from the wedge and adaptor leaks to the cooled CFC base plate by radiation (εeff.2 = 0.5) and by conduction via the Inconel feet. Finally, the heat accumulated in the CFC base plate leaves its structure to the supporting plate via the toroidal strip contacts by conductance. The discussed physical model of the thermal process could be described by a well-known equation for the 3D transient non-linear heat conduction problem with the following boundary conditions: ∂t(x, y, z) = qabsorb − qrad ∂n
− for the lamellae upper surface (4.1)
∂t(x, y, z) =0 ∂n
∂t(x, y, z) = −qrad ∂n
t(x, y, z)
base/ sup
− for the divertor lateral surfaces − for the lower wedge surface
= T0
(4.2) (4.3)
− for the CFC BP/supporting plate
contact area
(4.4)
Fig. 3. Heat loading scheme in the JET machine for the cyclic analysis.
This heat load of 5.0 MW/m2 for the spatial conical surface can be recalculated for the total area of upper metallic surfaces of lamellae, including all shadowed and wetted areas on the top surfaces (this is how the load is applied to the FE model). This re-calculation yields a heat load of 6.43 MW/m2 × 10 s for metal. The pulse repetition time is 1800 s. So, for the cyclic analysis under the averaged uniform heat loading it is assumed that during 10 s the upper surfaces of the divertor tiles are loaded with a uniform heat flux of 6.43 MW/m2 . And during a pause of 1790 s the divertor is cooled down passively by (a) radiation to the FW (εeff.1 = 0.25) and base plate (εeff.2 = 0.5) and (b) conduction to the base plate/supporting plate contact area.The cyclic loading reflecting the time needed to gain quasi-steady-state conditions (5 pulses) can be written as:
Here:
- t(x,y,z)|=0 = T0 is the divertor initial temperature; 4 ) is the heat flux lost to the in- qrad = εeff ϕ(T 4 (x, y, z) − Tsurroundings
vessel components by radiation, where = 5.67 × 10−8 W/m2 K4 ; - T(x,y,z) = t(x,y,z)ext surf is the divertor external surface temperature; is the effective emissivity defined as - εeff εeff = 1/(1/εtile + 1/εsurroundings − 1); - ϕ = 1 is the geometric configuration factor between the divertor surface and the surfaces of the in-vessel components.
Tsurroundings =
200◦ C, for the upper surface; Tbase plate, for the lower surface;
T0 = 35 ◦ C; qabsorb () = 6.43 MW/m2 ×
1, for ∈ pulse 0, for ∈ pause.
855
2
qload = 6.43 MW/m ×
1, 0,
1800n ≤ ≤ 1800n + 10 , 1800n + 10 < < 1800(n + 1)
where n = 0–5 is the number of pulses.
4.2. Realistic heat loading Fig. 4 describes of input thermal loads used to analyze thermal transients in the divertor structure taking into account the global and local shadowing effect (cf. [8]). The discussed input loads are consistent with those described in the previous section, but, of course, specific power density for the lamellae exposed to the heat loads is higher than an average power for all lamellae, since some other lamellae are unloaded due to stack-to-stack shadowing effects and other reasons.
4.1. Loading conditions The current analysis is performed for the static configuration of heat loads. This means that no sweeping effects (double exposition at the edges, different repetition time for the tile centre and tile edges, etc.) have been analyzed. An input load for the thermal analysis (surface density of the thermal power and energy) is specified as 5.0 MW/m2 × 10 s, where the area is the entire conical surface (frustum) covering the divertor row, including all gaps and top surfaces of all lamellae with all wetted and shadowed areas (see Fig. 3). JET originally specified this value as independent of the field angle and constant with the radial coordinate.
Fig. 4. Shadowing effect for lamellae nominal position.
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Fig. 7. Evolution of the maximal temperature of the JET divertor. Fig. 5. FE global model of the JET divertor. Mesh.
The cyclic analysis under the averaged heat loading makes it possible to determine, first, the number of machine operational cycles to attain the quasi-steady-state conditions of the divertor temperatures and, second, the maximal temperatures attainable by different divertor components: lamella, wedge, chain, adaptor and base plate in order to confirm their workability as it is or to outline the range of acceptable operational conditions.
Fig. 7 illustrates the JET divertor temperature response (lamella maximal temperature) to the cyclic loading conditions. One can see from the temperature curve shown in this figure that the quasisteady-state conditions are gained in five cycles. Hand in hand with the reaching a quasi-steady-state condition with the number of pulses (1) the divertor maximal temperature increases from 1387 ◦ C up to 1915 ◦ C (Fig. 8) and (2) the divertor residual temperature will also increase from 374 ◦ C to 615 ◦ C. The wedge temperature spatial distribution shown in Fig. 9 demonstrates evidently that the wedge area contacting the lamellae “legs”, even though protected with thermal insulating (ZrO2 ) strips, attains ∼1055 ◦ C. The wedge reaches its maximal temperature 40 s after the beginning of exposure to the specified plasma, for each pulse. The area with the highest chain temperature is represented by the chain plugs, in contact with the side lamellae. A maximum temperature of 696 ◦ C is attained at the end of the pulse, i.e. in 10 s. The maximum temperature of the chain–rail assembly shifts with time from the plugs down to the anchors, where it reaches 234 ◦ C at the end of the first cycle. Starting from the second cycle, temperature states of the chain assembly are different for the upper and lower stacks due to nonequality of their residual temperatures before the second pulse. The chain temperature difference is as high as ∼330 ◦ C at the fifth operational cycle. If the most part of the chain structure attains a temperature of 1000–1100 ◦ C in 40 s of the last cycle, the temperaturevulnerable spring elements will not exceed 620 ◦ C during, at least, the first five pulses of the machine operation (Fig. 10). Note that a
Fig. 6. FE model of the wedge and adaptor. Mesh.
Fig. 8. Temperature state of the JET divertor assembly at the end of fifth pulse: = 7210 s; max temp: 1915 ◦ C.
5. Description of the ANSYS model The 3D FE ANSYS model [9] of the JET divertor unit (Figs. 5 and 6) was developed to simulate the divertor temperature response to the pulsed surface heat load. The model consists of 455 091 elements. A thermal mass solid, an 8-node brick, SOLID70 is the basic type of model elements applied for the transient thermal analysis. Together with the basic SOLID70, the thermal element SHELLl57, SURF152 and superelement MATRIX50 were used to build-up the 3D ANSYS model of different elements composing the JET divertor unit and to simulate the heat exchange process by radiation. 6. Calculation results and discussions 6.1. Cyclic analysis under the averaged heat loading of 6.43 MW/m2
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857
Table 2 Heat loading options.
Fig. 9. Temperature state of the divertor carrier (wedge) in 40 s after plasma start-up (fifth pulse): = 7240 s; max temp: 1055 ◦ C.
Lamellae position Field angle
Nominal, full power
1◦ 4◦
LWF = 0.60, Plocal = 26.8 MW/m2 LWF = 0.77, Plocal = 11.9 MW/m2
increase of its heat flux values. To evaluate the influence of the “shadowing” effect the real loading conditions taking into account the lamella wetted fraction are simulated according to the calculation scheme shown in Fig. 4. Table 2 summarizes all calculation options analyzed in the performed study. The obtained results are shown in Figs. 11 and 12 and in Table 3. Here, one can find the pictures demonstrating the influence of the “shadowing effect” on (1) the JET divertor, (2) wedge and (3) chain assembly temperature states. It is clear from Fig. 11 that the lamellae could survive only 7.25 s of the heat load determined for the nominal lamella position and a field angle of 1◦ (q1◦ = 26.788 MW/m2 ). Just after 6 s of the plasma burning start-up the lamellae surface attains a tungsten melting temperature of ∼3400 ◦ C. A heat loading angle of 4◦ (q4◦ = 11.927 MW/m2 ) allows for the lamella to withstand a straight loading cycle of 10 s for the whole range of the specified power for the nominal lamella position (Fig. 12).
Fig. 10. Temperature state of chain assembly at the end of fifth cycle. (Stack 1. = 9000 s. Max temp: 615 ◦ C).
more sensible temperature limit for the spring elements amounts to 500 ◦ C, which reduces the number of such pulses to about 2, depending on the inter-shot cooling time. The temperature of the chain side covers (1280 ◦ C) approaches the Nimonic melting point of 1345 ◦ C at the end of the fifth pulse (7210 s). The thermal analysis showed that 2 mm ceramic washers placed below the oval cover plates make it possible to reduce the maximal temperature attainable by the chain covers from 1280 ◦ C down to ∼1060 ◦ C. Table 1 gives the maximal temperatures gained by different components of the JET divertor unit during the cyclic operation at the averaged heat loading q = 6.43 MW/m2 . 6.2. Cyclic analysis under the realistic heat loading (GWF&LWF) The “shadowing” effect (Fig. 4) causes a non-uniform heat load distribution over the lamellae upper surface and a subsequent Table 1 Summary of peak temperatures (◦ C) for divertor components. No.
1. 2. 3. 4. 5.
Component
Lamella Wedge Adaptor Chain Base plate
Heat flux = 6.43 MW/m2 First pulse
Last pulse
1387 613 166 696 54
1915 1055 312 1280 67
Fig. 11. JET divertor (a) and wedge (b) temperature state at ϑ = 1◦ , GWF = 0.4 & LWF = 0.6, =8 s: lamella − Tl.max = 3441 ◦ C; (b) wedge − Tw.max = 476 ◦ C.
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S. Grigoriev et al. / Fusion Engineering and Design 84 (2009) 853–858 Table 3 Summary of the thermal analysis.
Lamella ϑ = 90◦ ϑ = 4◦ ϑ = 1◦ Wedge ϑ = 90◦ ϑ = 4◦ ϑ = 1◦
GWF
LWF
Heat (MW/m2 )
Time (s)
Max temp (◦ C)
1 0.7 0.7 0.4 0.4
1 1 0.77 1 0.6
6.43 9.18 11.9 16.07 26.79
10 10 10 10 8
1387 1959 2228 3164 3440
1 0.7 0.7 0.4 0.4
1 1 0.77 1 0.6
6.4 9.18 11.9 16.07 26.79
40 40 40 40 8
615 831 830 1281 476
from ∼7.25 s to 2.75 s (for a field angle of 1◦ , full power heat and the lamella nominal position). 7. Conclusions The thermal analysis in support of the JET divertor unit makes possible the following conclusions. The current design of the JET divertor unit provides more favourable operation conditions for the temperature-vulnerable materials of the stack attachment thereby increasing the attachment lifetime. Thus, the model simulation performed shows that the JET divertor unit is capable to withstand a couple of full-energy cycles with an averaged heat flux of 6.43 MW/m2 following at a 30min repetition time. Up to five cycles indeed if we would consider the melting points as being the limit (a reserve factor has obviously to be specified). However, if we take into account (i) the real heat load distribution over the upper lamellae surface (shadowing effect even at the lamellae nominal, i.e. non-elevated position); (ii) an initial temperature of the divertor structure of 200 ◦ C (instead of 35 ◦ C) after the baking procedure; (iii) possible uncertainties as to the material properties and calculation accuracy, it may be that the temperature approaches 600 ◦ C after a single full-energy pulse. Acknowledgements This work, supported by the European Communities under contracts between EURATOM and Forschungszentrum Jülich, was carried out within the framework of the European Fusion Development Agreement (EFDA). The views and opinions expressed herein do not necessarily reflect those of the European Commission. References
Fig. 12. JET divertor and its components temperature state at ϑ = 4◦ , GWF = 0.7 & LWF = 0.77, = 10 s: lamella − Tl.max = 2228 ◦ C; (b) wedge − Tw.max = 830 ◦ C; (c) chain − Tc.max = 825 ◦ C.
It should be noted that the results presented in Figs. 11 and 12 reflect the influence of the heat loads “shadowing” on the JET divertor temperature state in case of heat loading onto the “cold” divertor unit (the divertor initial temperature before heat loading equals to 35 ◦ C). For quasi-steady state conditions (the divertor residual temperature is ∼600–700 ◦ C), the lamella lifetime (an operation time to attain the tungsten melting temperature) is reduced significantly:
[1] Thermal analysis of the JET LB-SRP divertor, Final Report, January 2007 (Internal JET-EFDA document). [2] Ph. Mertens, T. Hirai, J. Linke, O. Neubauer, G. Pintsuk, V. Philipps, S. Sadakov, U. Samm, B. Schweer, Fusion Eng. Des. 82 (2007) 1833–1838. [3] Ph. Mertens, H. Altmann, T. Hirai, M. Knaup, O. Neubauer, V. Philipps, J. Rapp, V. Riccardo, S. Sadakov, B. Schweer, A. Terra, I. Uytdenhouwen, U. Samm, Fusion Eng. Des, doi:10.1016/j.fusengdes.2008.11.055, submitted for publication. [4] Densamet is a registered trademark of MG Sanders Ltd., Stone, U.K. [5] Ph. Mertens, JET W-bulk Team, in: T. Hirai, Ph. Mertens (Eds.), Conceptual design for a tungsten bulk LB-SRP, Final Report, March 2006 (internal JET-EFDA document). [6] T. Hirai, H. Maier, M. Rubel, Ph. Mertens, R. Neu, O. Neubauer, et al., R&D on full tungsten divertor and beryllium wall for the JET ITER-like Wall Project, Fusion Eng. Des. 82 (2007) 1839–1845, doi:10.1016/j/fusengdes.2007.02.024. [7] ITER Material Properties Handbook, ITER Document No. S74 RE 1. [8] J. Rapp, G. Pintsuk, Ph. Mertens (on Power Handling of the LBSRP), in press. [9] ANSYS Release 10.0.