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CFD analysis of the ITER first wall 06 panel. Part II: Thermal-hydraulics
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CFD analysis of the ITER first wall 06 panel. Part II: Thermal-hydraulics R. Zanino a , R. Bonifetto a , F. Cau b , A. Portone b , L. Savoldi Richard a,∗ a b
Dipartimento Energia, Politecnico di Torino, 10129 Torino, Italy Fusion for Energy, 08019 Barcelona, Spain
a r t i c l e
i n f o
Article history: Received 15 October 2013 Received in revised form 26 March 2014 Accepted 28 March 2014 Available online xxx Keywords: Nuclear fusion ITER First wall Thermal-hydraulics CFD
a b s t r a c t The computational fluid dynamics (CFD) analysis of the FW06 panel of the ITER shielding blanket is presented in two companion papers. In this Part II we concentrate on the thermal-hydraulics of the water coolant, driven by the nuclear volumetric and plasma surface heat loads discussed in Part I. Both the detailed steady state analysis of a single cooling channel and the coarse transient analysis of the whole panel are considered. The compatibility of the hot spots with the maximum recommended temperatures for the different materials is confirmed. The heat transfer coefficient between coolant and walls is obtained post-processing the results of the simulation and compared with the results of available correlations, which may be used for simpler analyses: in the fully developed flow regions of the cooling pipes, it turns out to be well approximated by the Sieder–Tate correlation. The operation margin with respect to the critical heat flux is also computed and turns out to be sufficiently large compared with the design limit. © 2014 Elsevier B.V. All rights reserved.
1. Introduction The ITER shielding blanket will be made of 440 blanket modules (BM), ∼4 tons each, attached to the inner shell of the vacuum vessel [1], see Fig. 1a. The BMs are arranged in 18 rows numbered poloidally starting from the lowermost inboard (#01) and ending with the lowermost outboard (#18), see Fig. 1b. Different rows will be subject to different surface heat loads, so that they are grouped in two categories: normal heat flux (below 2 MW/m2 ) and enhanced heat flux (up to 4.7 MW/m2 ) [2]. Each BM is actively cooled by highly sub-cooled pressurized water at ∼70 ◦ C and 4 MPa, inlet temperature and pressure, respectively, in forced circulation. Each BM is made of a first wall (FW) panel, exposed directly to the plasma, and of a shield block (SB), to which the FW is attached, see Fig. 1c. Here, following the hydraulics study presented in Part I [3], we address the question of the thermal-hydraulics of the FW06 panel (belonging to a normal heat flux BM), under the combined action of the nuclear volumetric and plasma surface heat loads presented in Part I. The main objectives of this Part II are: • To verify the presence of hot spots and check their compatibility with the different materials (the maximum recommended values are, respectively [4]: 660 ◦ C for the Be, 350 ◦ C for the CuCrZr and 450 ◦ C for the stainless steel);
• To compute the heat transfer coefficient (HTC) everywhere and to assess the reliability of the available correlations, which may be used for simple analyses; • To check the operation margin with respect to the critical heat flux (CHF) in the hottest channels. The commercial computational fluid dynamics (CFD) code ANSYS-FLUENT [5] will be adopted for the thermal-hydraulic analysis, considering the improved geometry which came out of the hydraulic analysis presented in Part I. The similar approach, splitting hydraulics and thermal-hydraulics, was recently successfully used also for other large ITER components, like the vacuum vessel [6,7]. The analysis presented in the paper focuses on two major items: in Section 2 we present the steady-state thermal-hydraulic study of a single cooling channel, out of the 16 present in the FW06 panel; two distributions of the surface heat load (uniform and peaked) are considered and two different geometries, with or without thin stainless steel pipes embedded in the CuCrZr heat sink: in the case with the pipes, a fine mesh, see the companion Part I of this paper, is needed and it can be afforded thanks to the limited size of the domain; in the case without pipes, a coarse mesh (see again Part I) is sufficient. In Section 3 the transient thermal-hydraulic study of the whole panel is presented, using a coarse mesh, which is justified in the case of uniform surface heat load by the single-channel study presented in Section 2. 2. Single-channel steady-state thermal-hydraulic analysis
∗ Corresponding author. Tel.: +39 011 090 4447; fax: +39 011 090 4499. E-mail address: [email protected] (L. Savoldi Richard).
We cut away a limited portion of the panel, consisting of a single cooling channel. The channel under study is located in the
http://dx.doi.org/10.1016/j.fusengdes.2014.03.088 0920-3796/© 2014 Elsevier B.V. All rights reserved.
Please cite this article in press as: R. Zanino, et al., CFD analysis of the ITER first wall 06 panel. Part II: Thermal-hydraulics, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.03.088
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Fig. 1. Location and structure of the ITER blanket module 06.
center of the panel and is broadly representative, as far as the geometry is concerned and with the only exception of the inner manifold shapes, of most of the other channels, but for the four lateral ones (C1, C8, C9 and C16, see [3]). Simplified BCs are assumed here and namely the adiabatic boundaries of the single channel toward both the neighboring channels and the I-beam. A steady state thermal-hydraulic analysis of the entire FW06 panel is presented in Appendix A to confirm the suitability of this assumption. The inlet temperature (70 ◦ C) and mass flow rate are imposed as BCs, together with the outlet pressure. For both the case with and without thin stainless steel pipes, the 3D temperature distribution in the structure has been determined, for each of the two different surface heating scenarios discussed in Part I. The results obtained with and without pipes will be compared below, in order to check for which of the two surface heat load distributions, if any, the global adequacy of the model without pipes is confirmed. That
is indeed the only affordable model for the whole-panel transient analysis, from the point of view of the needed mesh. 2.1. Uniform surface heat load 2.1.1. Temperature maps In Fig. 2 we show the comparison between the temperature maps on the tile surface computed without and with thin SS pipes, while in Table 1 a more punctual comparison can be performed, where the peak temperature values computed in the two cases are reported for different regions in the computational domain. In Fig. 2 it may be noted that the two maps are qualitatively similar, with progressively increasing tile temperature along the flow path, but the average surface temperature is higher in the case with SS pipes, see Fig. 2, due to their additional thermal resistance. On the contrary, the two peak temperatures on the tile surface are
Fig. 2. Temperature map (◦ C) of the tile surface computed without (a) and with (b) thin SS heat pipes embedded in the CuCrZr heat sink, respectively, in the case of uniform surface heat load.
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Fig. 3. (a) Temperature map (◦ C) of the surface of the fluid domain in the inner manifold region, computed in the case with thin SS pipes embedded in the CuCrZr heat sink and uniform surface heat load. (b) Toroidal cross section of the FW06 panel at the level of the inner manifold: material composition from the top (plasma) side: Be tiles (yellow), Cu compliance layer (blue), CuCrZr heat sink (green), stainless steel support (red) also around the inner manifold, and water coolant (cyan). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Table 1 Peak temperature values (◦ C) at different locations, computed without and with thin SS pipes embedded in the CuCrZr heat sink,a in the case of uniform surface heat load. Location
Without thin SS pipes
With thin SS pipes
Tile surface Interface between tiles and Cu layer Interface between Cu and CuCrZr layers SS pipes in CuCrZr sink Water (in the pipes) Water (average on outlet section)
195.1 174.5 172.5 – 131.5 104.7
195.1 172.9 171.3 140.0 128.7 104.4
a
Two different meshes are used in the two cases, see Part I [3].
identical in the two cases, see also Table 1, and this can be understood looking at the location of the peak temperature, which is on the tile(s) close to the panel centerline on top of the inner manifold, see also Fig. 3a below, where the SS pipes are not present. The poor heat removal capability in that region is a combination of the poor flow at that location, see Part I, and of the layer structure of the different materials, with more (poorly conductive) SS and less (highly conductive) CuCrZr below the tiles in that region, see Fig. 3b below. As far as the water temperature is concerned, the peak in the pipes is higher in the case when the thin SS pipes are not included in the model, as expected. Note, however, that when the thin SS pipes are included in the model, the peak water temperature is located in the inner manifold, see Fig. 3a. The computed peak temperature in the Be tiles is well below the acceptable ITER limit of 660 ◦ C. The temperature map computed on the surface of the fluid domain (inlet section + outlet section + walls) using the fine mesh is shown in Fig. 4. The pattern of progressive increase of the temperature while moving along the hydraulic path is clearly observed, except for the peaking of the temperature again in the inner manifold of the central finger, see Fig. 4a. A zoom of the temperature map computed on the inner manifold wall using the fine mesh is shown in Fig. 3. It is seen that the temperature on the second and third manifolds varies by ∼50 ◦ C when going from the region just below the hottest tiles to the SS support on the back of the panel. The shape of these two manifolds, improved in order to reduce the stagnation regions, forbids any sort of mixing between the water in the back and below the tiles. In Fig. 5 we report the temperature map computed on a section cutting the water in the first and third outer manifolds, when the thin SS pipes are included in the model. The effect of the inflow of
Fig. 4. Temperature map (◦ C) of the surface of the fluid domain (inlet + outlet + walls) computed in the case with thin SS pipes embedded in the CuCrZr heat sink and uniform surface heat load: (a) front (plasma side) view; (b) back view.
cold water from the couple of pipes in the CuCrZr sinks is clearly visible, while the surrounding water is hotter due to the direct heating on the manifolds themselves. In view of the relatively low heat conductivity of SS a large temperature difference arises between the outer and inner radius of the SS pipes embedded in the CuCrZr heat sink, which may give rise to non-negligible thermal stress. Our simulations show that the maximum temperature difference occurs in the last finger. On the plasma side of the pipe the temperature varies by ∼10 K on the pipe thickness (0.5 mm), while its variation remains below 5–6 K on the back side, see Fig. 6. As a final remark on the detailed comparison between the temperature maps computed with and without SS pipes embedded in the CuCrZr heat sink, we can state that the results obtained in the two cases are within ∼10% of each other, in terms of temperature increase with respect to the coolant temperature at the inlet. We thus consider the model without SS pipes to be an acceptable
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Fig. 7. Map of the wall heat flux (W/m2 ) to the water coolant, in the case of uniform surface heat load computed including the thin SS pipes in the model.
Fig. 5. Temperature maps (◦ C) on a cross section of the fluid domain in the first (a) and third (b) outer manifold region, computed using the fine mesh in the case of uniform surface heat load.
approximation in the case of uniform surface heat load. It is then justified to use below the similar approximation for the study of the thermal-hydraulic transient in the whole FW06 panel, under uniform surface heat load. 2.1.2. Heat transfer coefficient We now move to the post-processing of the results above in terms of HTC, which is defined as HTC =
Wall heat flux [W/m2 ] (Twall − Tbulk ) [K]
(1)
The wall heat flux to the water is reported in Fig. 7, on a scale from zero to the maximum value of 0.65 MW/m2 , where positive values represent the regions where the water is cooling the structure (in some limited portion of the sides of the boxes of the inner manifolds the water actually heats the solid, not shown, giving rise to a negative heat flux).
As far as the pipes are concerned, it is straightforward to postprocess the computed results evaluating first the average wall heat flux (Fig. 8a), wall temperature and water bulk temperature (Fig. 8b) at selected axial locations along the pipe and then applying (1) to obtain the profile of the HTC along the hydraulic path in each finger (Fig. 8c), to be compared with the results of available correlations (Fig. 8c). In Fig. 8a we note that the peak and average fluxes differ significantly only in the small pipes embedded in the CuCrZr heat sink, as they are most exposed to the one-sided heat flux from the plasma. On the contrary, in the larger pipes embedded in the SS support the wall heat flux is roughly uniform on each cross section thanks to the homogenizing action of heat conduction in the different solid structures. In Fig. 8b we see that the bulk water temperature progressively increases from the inlet to the outlet of the channel. On the other hand, the wall temperature is more sensitive to the location of the pipe with respect to the heated tiles, resulting in two distinct increasing profiles along the small pipes and along the large pipes. In Fig. 8c we see that the HTC coming from the post-processing of the CFD results roughly falls in the range (0.5–1.5) × 104 W/(m2 K) and is typically well (and in any case conservatively) approximated by the HTC coming from the Sieder–Tate correlation [8]. Consistently with the fact that this correlation requires the turbulent flow to be fully developed, we cannot expect it to apply when entry effects are still relevant. The CFD results predict an HTC which is larger than that coming from the correlation due to the presence of swirled flow at the beginning of the pipes, see Fig. 9, which enhances the heat transfer. Deducing an HTC in the case of the inner and outer manifolds is much less straightforward than in the case of the cooling pipes, because of the ambiguity in the definition of the bulk water temperature. If we try to extract a single value of HTC from averaged values of temperature and wall fluxes over each manifold, we find HTC up to several tens of W/(m2 K). On the other hand, if we should use the FLUENT diagnostic for the HTC, which returns the ratio between the wall heat flux and the temperature difference between the wall and the adjacent fluid cell [5], we would find HTC up to several thousands of W/(m2 K). This ambiguity cannot, unfortunately, be easily resolved. 2.2. Peaked surface heat load
Fig. 6. Temperature map (◦ C) on the cross section of an SS pipe (last finger, central location along the finger), in the case of uniform surface heat load.
Also for the case with peaked surface heat load, the simulations have been run both with and without thin SS pipes. However, in view of the fact that the case without SS pipes is mainly relevant for the transient analysis of the entire FW06 panel below, where only the uniform surface heat load case will be considered, we concentrate here on the discussion of the results obtained with SS pipes, unless otherwise noted.
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Fig. 9. Evidence of swirl flow near the entrance of the cooling pipes, from the computed path lines drawn from the fluid inlet and colored by fluid speed, in the case of uniform surface heat load (thin SS pipes included in the model).
peak of the surface heat load is located and on the third (hottest) finger of the hydraulic series, see Fig. 10a, as expected. The temperature gradient across the finger, moving away from the plasma, is significant: ∼180 K across the 1 cm tile thickness (i.e., a comparable gradient to that seen on the thin SS pipes in the uniform surface heat load case), and ∼10 K across the 2 mm Cu layer. The peak surface temperature of the water, again located below the peak surface heat load at the finger knee, see Fig. 10b, is ∼225 ◦ C, which is below the saturation temperature at the operating pressure (∼250 ◦ C). The comparison between peak temperature values in different regions of the FW06 panel, obtained for the peaked surface heat load, without and with thin SS pipes, is reported in Table 2. While obviously the (bulk or average) water temperature is only marginally influenced by the presence of the SS pipes, the peak temperature values on the tiles, Cu compliance layer and CuCrZr sink are dramatically influenced by the neglection of the thermal resistance contributed by the SS pipes. In particular, the peak temperature increase on the tiles is underestimated by ∼50 K when using the coarse grid, although in relative terms this is “only” ∼15% of the total temperature increase of the tiles. It may therefore be concluded that a model neglecting the thin SS pipes should not be fully adequate for the study of the thermal-hydraulic effects of a peaked surface heat load. (The presence of the latter could still be approximately taken into account, even in a model of the whole panel and with a relatively coarse mesh, by introducing an ad hoc thermal resistance between the CuCrZr and the water fluid domain.) In all cases the peak Be temperature is always below the acceptable maximum of 660 ◦ C. We now proceed and evaluate the temperature difference across the thickness of the SS pipes. The hottest point in the SS pipes is located below the surface heat load peak, as expected, see Fig. 11. The maximum temperature difference across the pipes also occurs below the load peak, on the last finger, reaching ∼45 K, see Fig. 11. 2.2.2. HTC and CHF margin Starting from the averaged wall heat flux (not reported here) and from the wall and bulk temperature, suitably averaged over
Fig. 8. Computed profiles along the hydraulic paths in each finger, including the thin SS pipes in the model, in the case of uniform surface heat load. (a) Wall heat flux: average (solid), peak (dashed). (b) Wall temperature (solid), bulk water temperature (dashed). (c) HTC: from the post-processing of the CFD simulation (solid), from the Sieder–Tate correlation (dashed).
2.2.1. Temperature maps The temperature maps computed on the tile surface and on the surface of the fluid domain are shown in Fig. 10. The peak temperature value on the channel is reached on the tiles where the toroidal
Table 2 Peak temperature values (◦ C) at different locations, computed without and with thin SS pipes embedded in the CuCrZr heat sink,a in the case of peaked surface heat load. Location
Without thin SS pipes
With thin SS pipes
Tile surface Interface between tiles and Cu layer Interface between Cu and CuCrZr layers SS pipes in CuCrZr sink Water (in the pipes) Water (average on outlet section)
443.3 267.3 256.1 – 223.7 127.2
492.7 310.7 300.7 269.8 228.5 127.2
a
Two different meshes are used in the two cases, see Part I [3].
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Fig. 10. Temperature maps (◦ C) computed including the thin SS pipes in the model, in the case of peaked surface heat load: (a) tile surface; (b) water surface.
The critical heat flux (CHF) margin has been evaluated starting from the definition of CHF at the fluid wall, which can be evaluated from the simulation results following the definitions given in [9]. The CHF margin (CHFM) has been computed at each selected section, for the sink pipes as well as for the SS support pipes, as CHFM =
CHF Wall Heat Flux
(2)
For the denominator of (2), the peak heat flux at the selected section was considered. The resulting distribution of the CHFM in the case of the peaked surface heat load is reported in Fig. 12c. The CHFM decreases where the surface heat load peaks, and the minimum value (computed adopting in (2) the peak wall heat flux) is ∼5.7, which is well above the design requirement of 1.4 retained in the BM. 3. Whole-panel transient thermal-hydraulic analysis Fig. 11. Temperature map (◦ C) in the thin SS pipe thickness (last finger, central location along the finger), in the case of peaked surface heat load.
the perimeter and cross section, respectively (see Fig. 12a), the HTC has been computed from (1) and is reported in Fig. 12b. The temperature profile along each portion of the different fingers clearly keeps memory of the localized surface heating, showing a peak below the location of the surface load peak, even on the back side (SS support pipes), see Fig. 12a. The computed HTC is again on average well approximated by the HTC derived using the Sieder–Tate correlation, see Fig. 12b – the enhancement of the HTC due to the flow swirl is visible also in this case. It is also interesting to note that the value of the HTC is not very different from what obtained above in the case of uniform surface heat flux, which confirms the correctness of the recipe at least in a case like the present one, where the heating does not determine a dramatic change in the flow field driven by the pumps.
We analyze here the thermal-hydraulic response of the whole FW06 panel, when subject to the transient heat load scenario, corresponding to a standard plasma pulse, as presented in Part I. The surface heat load is assumed to be uniform and reaches 0.35 MW/m2 during the flat top. A series of pulses is analyzed to check the achievement of a periodic thermal-hydraulic response of the panel as well as of possible steady-state conditions during each pulse. The mass flow rate distribution among the different channels shows a limited non-uniformity similar to what obtained in the pure hydraulic simulations [3], consistent with the fact that the uniform heat load (surface + nuclear) cannot significantly affect the flow pattern in the FW06 panel. The temperature evolution in the different solid materials and in the coolant is computed and reported below. A sensitivity study on the time stepping and on the selected solution algorithm shows that the computed temperature maps are reliable within few percent in the worst case, see Appendix B.
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Fig. 13. Evolution of different variables during the first 13 plasma pulses: (a) Water outlet temperature (◦ C); (b) Max water temperature (red dashed), max Inconel temperature (blue solid), average SS temperature (◦ C) at SOB (triangles) and at EOB (circles). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 12. Computed profiles along the hydraulic paths in each finger, including thin SS pipes in the model, in the peaked surface heat load case: (a) Wall temperature (solid), bulk water temperature (dashed). (b) HTC: from the post-processing of the CFD simulation (solid), from the Sieder–Tate correlation (dashed). (c) CHF margin with respect to the peak heat flux.
3.1. Time evolution The simulation has been run for 13 pulses, starting from the purely hydraulic steady state (no energy equation), see Part 1. The evolution of some of the physical quantities that have been
monitored during the simulation, and namely the water outlet temperature, shown in Fig. 13 a, the water maximum temperatures, the SS average temperature at start of burn (SOB) and end of burn (EOB), shown in Fig. 13b, proves that periodic behavior is reached in most cases already after the 3rd pulse. Only the bolt peak temperature, also shown in Fig. 13b, has not reached a fully periodic behavior yet, although the residual increase of Tpeak in the bolt (∼343 ◦ C at the last EOB) between subsequent pulses is very small. The reason for this behavior is discussed below. The pressure drop across the whole FW06 panel stabilizes during the flat top and dwell periods at ∼0.93 bar after the 3rd pulse. This value is slightly larger than the value obtained in the purely hydraulic study presented in Part I, where the fluid temperature was assumed to be constant and equal to 100 ◦ C (instead of the average ∼80–85 ◦ C found in this case). The evolution of the average temperature of different materials during the 13th pulse is shown in Fig. 14, together with the maximum tile surface temperature. Notice that the SS average temperature is still slightly increasing at the end of the heating phase, driven by the Inconel temperature evolution, which is completely unsteady during the whole duration of the pulse. For the sake of completeness we mention that, in three different regions in the solid computational domain, an oscillatory behavior appears during the heating phase, but disappears as the power
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Fig. 14. Evolution of the average temperature (◦ C) of different materials during the 13th plasma pulse: (a) Cu, CuCrZr, SS, Inconel, water; (b) Be (the maximum tile surface temperature is also shown, solid line).
Fig. 15. Temperature maps (◦ C) at SOB: (a) equatorial cross section of the FW06 panel; (b) equatorial cross section of bolt and washer.
is switched off in the dwell phase. The monitored peak temperature values of Cu, CuCrZr and SS in these regions suffer of this oscillatory behavior, possibly due to small mesh defects, but the oscillations remain localized in a negligible portion of the computational domain for the whole transient. 3.2. SOB We discuss here the computed solution at the end of the 13th pulse. This is at the same time the end of the dwell period and the start of burn (SOB) for the subsequent pulse. Fig. 15a shows that the surface of the tiles is well cooled and returns to its initial temperature (∼70 ◦ C, coincident with the coolant inlet temperature), before the beginning of a new pulse. On the other hand, the bolt turns out to be the worst cooled region, see also the zoom in Fig. 15b. The bolt is heated by the nuclear volumetric heat load and on its top surface it is also subject to the surface heat load. As on the lower part of the panel, including the bolt, an adiabatic BC was (very conservatively) imposed, the bolt can only be cooled by thermal conduction through the washer. (To avoid assuming adiabatic boundary conditions between bolt and SB, one could include in the model the SB insert where the central bolt is screwed in and prescribe there suitable contact heat transfer coefficients [4].) The washer refrigeration is again provided only by conduction through the thin cylindrical wall of the lower part of the I-beam, resulting in quasi-1D temperature profiles in both regions. Since the active cooling is far away from this part of the I-beam, the region of the bolt and washer is not as well cooled as the rest of the panel. The result is that the bolt temperature needs many more pulses than any other region of the FW06 panel to reach a periodic behavior.
Fig. 16. Temperature map (◦ C) on the heated surface of the tiles at SOB (all temperature values above 215 ◦ C are represented as equal to 215 ◦ C in the figure).
Indeed, pulse after pulse the increase of the bolt temperature at periodic conditions of the rest of the I-beam allows increasingly better heat transfer and therefore faster recovery of the conditions at SOB in the bolt, see Fig. 13b.
3.3. EOB We discuss here the computed solution 400 s after the start of the 13th pulse, i.e. at the EOB. The temperature on the heated surface of the tiles is shown in Fig. 16. The repetitive 2D pattern directly reflects the single channel cooling paths.
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Fig. 17. Temperature maps (◦ C) at EOB: (a) equatorial cross section of the FW06 panel (all temperature values above 220 ◦ C are represented as equal to 220 ◦ C in the figure); (b) bolt and washer cross section.
Fig. 17a shows the temperature map on the equatorial cross section of the FW06 panel. The hot spot is again in the bolt, which also drives the local temperature increase in the surrounding stainlesssteel region. The inlet piping is of course always at 70 ◦ C. The detail of the temperature distribution on the bolt cross section is presented in Fig. 17b, where the peak in the lowest region, which is the worst cooled part, is clearly visible. Two other warm regions are identified in the contact zone between the supports and the I-beam, see the red ovals in Fig. 17a, where the local over-heating results from a combination of distance from active cooling regions and adiabatic BC assumed in the simulation on the I-beam back side, notwithstanding the lower heat deposition compared with the tiles. Fig. 18 shows two cross sections of the panel in the (x–z) plane, located in correspondence of the black lines in Fig. 17a, i.e. where the above-mentioned warm regions in the I-beam/support are located. It is clear that on these two cuts the highest temperatures are not reached on the tiles, but rather they are located in the back of the SS supports, in the last finger of each hydraulic channel. In Fig. 18, the cooling path of the water is also clearly visible, getting hotter as it moves downstream in the hydraulic series of the three fingers. The top and bottom maps do not show perfectly symmetric distribution because of the above-mentioned asymmetries in the mass flow rate distribution among the different channels. Notice also the hot spots on the tiles of the side fingers due to the larger distance between tile edge and cooling pipes. Fig. 19 shows the poloidal cross section of the I-beam at the midplane between A and B sides, where the temperature peak of ∼277 ◦ C is clearly visible in the top left corner and due to the ill cooling of that portion of the plate. A comparable hot spot is present in the back part in contact with the bolt.
Fig. 18. Temperature map (◦ C) at EOB on the two poloidal cuts identified by the black segments in Fig. 17: (top) side B; (bottom) side A.
Fig. 19. Temperature map (◦ C) at EOB on a poloidal cross section of the I-beam, at the midplane between side A and side B, excluding the bolt and the water coolant.
The asymmetry of the flow distribution between A and B side of the FW06 panel discussed above, induced by the bending of the inlet pipe, also reflects in an asymmetry of the temperature distribution in the central part of the I-beam and, therefore, in the inlet temperature to the channels, see Fig. 20.
Fig. 20. Temperature profiles (◦ C) at EOB: (a) back side of the fluid domain, including inlet pipe; (b) front (plasma) side of the I-beam, with the small inlet pipes to the different channels in the central part.
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4. Conclusions The comprehensive thermal-hydraulic model of the ITER FW06 panel has been developed within the ANSYS-FLUENT framework. Two problems have been considered: a single cooling channel at steady state, including most of the geometrical details, and a coarser but transient analysis of the whole panel. The main conclusions of the single-channel steady-state thermal-hydraulic analysis are: • If compared with the uniform surface heat load scenario at 0.35 MW/m2 , the case of peaked surface heat load at 2 MW/m2 , always combined with the volumetric nuclear heat load, leads as expected to more severe conditions for the FW06 panel: ◦ The temperature on the surface of the tiles reaches a maximum of ∼493 ◦ C (vs. ∼195 ◦ C in the uniform surface heat load case), which is however still well below the recommended maximum of 660 ◦ C. ◦ The temperature in the CuCrZr reaches a maximum of ∼300 ◦ C, which is below the recommended maximum value of 350 ◦ C. ◦ The maximum temperature difference across the thin stainless steel wall of the pipes embedded in the CuCrZr heat sink peaks at ∼45 K, vs. ∼10 K peak in the uniform surface heat load case. ◦ The minimum critical heat flux margin is ∼5 (vs. ∼30 in the uniform surface heat load case), which is however still well above the acceptable minimum of 1.4. • The heat transfer coefficient between water coolant and stainless steel pipes, at ∼(0.5–1.5) × 104 W/(m2 K), is well approximated by the Sieder–Tate correlation in the fully developed flow regions of the cooling pipes, while it further increases near the entrance of the pipes due to swirl flow effects. This result is independent of the surface heat load profile. • In the case of uniform surface heat load, neglecting the thin SS pipes in the model, as it is needed to do for the transient thermalhydraulic study of the entire FW06 panel, gives results which are reasonably close to those obtained including the thin SS pipes. In the case of peaked surface heat load, the two models give very different results. The main conclusions of the whole-panel transient thermalhydraulic analysis under uniform surface heat load are: • The thermal-hydraulic conditions in the FW06 panel become periodic after three pulses except for the bolt, whose peak temperature after 13 pulses is still slightly increasing, partly due to the (conservative) boundary conditions assumed in this study. The bolt temperature is also the only quantity of interest that does not reach a steady state during the pulse flat top • The following peak temperatures have been computed at EOB: ◦ ∼200 ◦ C on the tiles, well below the recommended limit of 660 ◦ C for Be; ◦ ∼170 ◦ C on the CuCrZr, well below the recommended limit of ∼350 ◦ C for this material; ◦ ∼280 ◦ C in a portion of the I-beam surface directly exposed to the plasma and poorly cooled, but still well below the recommended limit of 450 ◦ C for the stainless steel; ◦ ∼343 ◦ C in the Inconel (bolt and washer), which is the peak temperature in the whole FW06 panel, at the 13th pulse EOB (still slightly increasing). • The whole-panel (coarse mesh) transient results at EOB are in substantial agreement with the outcome of the fine-mesh single-channel steady-state analysis, in terms of tile temperature, as well as of HTC and CHF margin, thanks to the fact
that all of the relevant quantities (except the bolt and washer peak temperature, however obviously not included in the singlechannel analysis) reach a steady state during the pulse flat top. Acknowledgments The work at Politecnico di Torino was partially financially supported by F4E under contract F4E-2009-OPE-031-01-03. We thank F. Subba for implementing in FLUENT the routine for the nuclear heat load. We also thank an anonymous reviewer for several comments which led to an improvement of the quality of the paper. Appendix A. Whole-panel steady-state analysis The single-channel steady-state analysis presented above did not include the I-beam and assumed an adiabatic BC on the back of the SS support. In order to assess the adequacy of that assumption, which was needed due to the dramatic simplification of the computational domain with respect to the whole FW06 panel, we present here a few results of a whole-panel steady state analysis. Starting from the same pure hydraulic steady state condition adopted as initial condition for the whole-panel transient study, a steady state run is performed, with the nuclear + uniform surface heat load set constant at the flat top level. The following results refer to the solution obtained after 450 iterations. Fig. 21 contains a comparison of the temperature map computed on the heated surfaces of the tiles in three different cases: (a) the coarse-mesh steady-state single-channel computation presented in Section 2, (b) the whole-panel steady-state computation and (c) the whole-panel transient computation (results at EOB) presented in Section 3. The agreement between the three is shown to be excellent, giving a good indication of the adequacy of the single-channel boundary condition on the back of the SS support. The steady-state analysis of the whole panel allows computing the heat transfer between the support and the I-beam, which was neglected in the single-channel study. Referring to a single channel, it turns out that ∼1 kW goes from the I-beam to the support, which is small if compared with the ∼29 kW from the plasma onto the tile surfaces, on top of the ∼18 kW nuclear heat load. The adiabatic
Fig. 21. Temperature maps (◦ C) on the heated surface of the tiles of channel C13 (see part I [3]): (a) from the single-channel coarse-mesh computation presented in Section 2; (b) from the steady-state computation on the whole panel; (c) from the EOB solution of the whole-panel transient computation presented in Section 3.
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Appendix B. Numerical sensitivity study on the whole-panel transient results In order to assess the dependence of the presented results on different numerical parameters used for the transient simulation of the whole FW06 panel, a sensitivity study has been carried out. The values of four different variables, i.e. the maximum Inconel temperature increase (the most sensitive parameter), the outlet water temperature increase, the maximum water temperature increase and the water pressure drop, have been computed at the EOB of the first plasma pulse (t = 400 s) and the relative difference with respect to the maximum increase of that variable has been evaluated. Fig. 22a shows the sensitivity analysis with respect to the time step adopted. If compared with the solution obtained with the most refined discretization (t = 1 s), the relative error in the case of t = 5 s (which is the time step used for the analysis presented in Section 3) is within ∼4%. Concerning the maximum number of iterations per time step, Maxiter , Fig. 22b shows that the relative error in our results above (obtained with Maxiter = 5), with respect to the solution obtained with Maxiter = 20, is always within ∼4%. Concerning the choice of the numerical scheme, Fig. 22c shows that if we use the coupled pressure–velocity algorithm instead of the segregated scheme used above, or if we use the second order time scheme instead of the first order used above, the differences arising in the solution are always within 1.5%. Also the possible effect of the introduction of the acceleration of gravity has been checked, but the effect is shown to be negligible, as expected considering the relatively small temperature differences in the water and the fact that the flow direction is mainly toroidal (i.e., at constant height). References
Fig. 22. Results of the sensitivity analysis on the whole-panel transient thermalhydraulic solution: (a) relative error in different variables with respect to the results obtained with time step t = 1 s. (b) Relative error in different variables with respect to the results obtained with maximum 20 iterations per time step (c) Relative difference in different variables with respect to the results of the scheme adopted above (segregated + 1st order in time + no gravity).
assumption on the back of the SS support, adopted for the singlechannel computations in Section 2, can therefore be considered acceptable, with an error of a few %.
[1] A.R. Raffray, M. Merola, Overview of the design and R&D of the ITER blanket system, Fusion Eng. Des. 87 (2012) 769–776. [2] R. Mitteau, P. Stangeby, C. Lowry, M. Merola, Heat loads and shape design of the ITER first wall, Fusion Eng. Des. 85 (2010) 2049–2053. [3] R. Zanino, R. Bonifetto, F. Cau, A. Portone, L. Savoldi Richard, CFD analysis of the ITER first wall 06 panel. Part I: Model set-up and flow distribution, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.03.081. [4] G. Dellopoulos, Private communication, 2012. [5] FLUENT User Manual, version 13.0. [6] L. Savoldi RIchard, R. Bonifetto, S. Corpino, J. Izquierdo, R. Le Barbier, Yu. Utin, et al., CFD analysis of a regular sector of the ITER vacuum vessel. Part I: Flow distribution and pressure drop, Fusion Eng. Des. 88 (2013) 3272–3279. [7] R. Zanino, L. Savoldi Richard, F. Subba, S. Corpino, J. Izquierdo, R. Le Barbier, et al., CFD analysis of a regular sector of the ITER vacuum vessel. Part II: Thermal-hydraulic effects of the nuclear heat load, Fusion Eng. Des. 88 (2013) 3248–3262. [8] F.P. Incropera, D.P. DeWitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, Wiley, Singapore, 2006. [9] A.R. Raffray, J. Schlosser, M. Akiba, M. Araki, S. Chiocchio, D. Dreimeyer, et al., Critical heat flux analysis and R&D for the design of the ITER divertor, Fusion Eng. Des. 45 (1999) 377–407.
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Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
CFD analysis of the ITER first wall 06 panel. Part II: Thermal-hydraulics R. Zanino a , R. Bonifetto a , F. Cau b , A. Portone b , L. Savoldi Richard a,∗ a b
Dipartimento Energia, Politecnico di Torino, 10129 Torino, Italy Fusion for Energy, 08019 Barcelona, Spain
a r t i c l e
i n f o
Article history: Received 15 October 2013 Received in revised form 26 March 2014 Accepted 28 March 2014 Available online xxx Keywords: Nuclear fusion ITER First wall Thermal-hydraulics CFD
a b s t r a c t The computational fluid dynamics (CFD) analysis of the FW06 panel of the ITER shielding blanket is presented in two companion papers. In this Part II we concentrate on the thermal-hydraulics of the water coolant, driven by the nuclear volumetric and plasma surface heat loads discussed in Part I. Both the detailed steady state analysis of a single cooling channel and the coarse transient analysis of the whole panel are considered. The compatibility of the hot spots with the maximum recommended temperatures for the different materials is confirmed. The heat transfer coefficient between coolant and walls is obtained post-processing the results of the simulation and compared with the results of available correlations, which may be used for simpler analyses: in the fully developed flow regions of the cooling pipes, it turns out to be well approximated by the Sieder–Tate correlation. The operation margin with respect to the critical heat flux is also computed and turns out to be sufficiently large compared with the design limit. © 2014 Elsevier B.V. All rights reserved.
1. Introduction The ITER shielding blanket will be made of 440 blanket modules (BM), ∼4 tons each, attached to the inner shell of the vacuum vessel [1], see Fig. 1a. The BMs are arranged in 18 rows numbered poloidally starting from the lowermost inboard (#01) and ending with the lowermost outboard (#18), see Fig. 1b. Different rows will be subject to different surface heat loads, so that they are grouped in two categories: normal heat flux (below 2 MW/m2 ) and enhanced heat flux (up to 4.7 MW/m2 ) [2]. Each BM is actively cooled by highly sub-cooled pressurized water at ∼70 ◦ C and 4 MPa, inlet temperature and pressure, respectively, in forced circulation. Each BM is made of a first wall (FW) panel, exposed directly to the plasma, and of a shield block (SB), to which the FW is attached, see Fig. 1c. Here, following the hydraulics study presented in Part I [3], we address the question of the thermal-hydraulics of the FW06 panel (belonging to a normal heat flux BM), under the combined action of the nuclear volumetric and plasma surface heat loads presented in Part I. The main objectives of this Part II are: • To verify the presence of hot spots and check their compatibility with the different materials (the maximum recommended values are, respectively [4]: 660 ◦ C for the Be, 350 ◦ C for the CuCrZr and 450 ◦ C for the stainless steel);
• To compute the heat transfer coefficient (HTC) everywhere and to assess the reliability of the available correlations, which may be used for simple analyses; • To check the operation margin with respect to the critical heat flux (CHF) in the hottest channels. The commercial computational fluid dynamics (CFD) code ANSYS-FLUENT [5] will be adopted for the thermal-hydraulic analysis, considering the improved geometry which came out of the hydraulic analysis presented in Part I. The similar approach, splitting hydraulics and thermal-hydraulics, was recently successfully used also for other large ITER components, like the vacuum vessel [6,7]. The analysis presented in the paper focuses on two major items: in Section 2 we present the steady-state thermal-hydraulic study of a single cooling channel, out of the 16 present in the FW06 panel; two distributions of the surface heat load (uniform and peaked) are considered and two different geometries, with or without thin stainless steel pipes embedded in the CuCrZr heat sink: in the case with the pipes, a fine mesh, see the companion Part I of this paper, is needed and it can be afforded thanks to the limited size of the domain; in the case without pipes, a coarse mesh (see again Part I) is sufficient. In Section 3 the transient thermal-hydraulic study of the whole panel is presented, using a coarse mesh, which is justified in the case of uniform surface heat load by the single-channel study presented in Section 2. 2. Single-channel steady-state thermal-hydraulic analysis
∗ Corresponding author. Tel.: +39 011 090 4447; fax: +39 011 090 4499. E-mail address: [email protected] (L. Savoldi Richard).
We cut away a limited portion of the panel, consisting of a single cooling channel. The channel under study is located in the
http://dx.doi.org/10.1016/j.fusengdes.2014.03.088 0920-3796/© 2014 Elsevier B.V. All rights reserved.
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Fig. 1. Location and structure of the ITER blanket module 06.
center of the panel and is broadly representative, as far as the geometry is concerned and with the only exception of the inner manifold shapes, of most of the other channels, but for the four lateral ones (C1, C8, C9 and C16, see [3]). Simplified BCs are assumed here and namely the adiabatic boundaries of the single channel toward both the neighboring channels and the I-beam. A steady state thermal-hydraulic analysis of the entire FW06 panel is presented in Appendix A to confirm the suitability of this assumption. The inlet temperature (70 ◦ C) and mass flow rate are imposed as BCs, together with the outlet pressure. For both the case with and without thin stainless steel pipes, the 3D temperature distribution in the structure has been determined, for each of the two different surface heating scenarios discussed in Part I. The results obtained with and without pipes will be compared below, in order to check for which of the two surface heat load distributions, if any, the global adequacy of the model without pipes is confirmed. That
is indeed the only affordable model for the whole-panel transient analysis, from the point of view of the needed mesh. 2.1. Uniform surface heat load 2.1.1. Temperature maps In Fig. 2 we show the comparison between the temperature maps on the tile surface computed without and with thin SS pipes, while in Table 1 a more punctual comparison can be performed, where the peak temperature values computed in the two cases are reported for different regions in the computational domain. In Fig. 2 it may be noted that the two maps are qualitatively similar, with progressively increasing tile temperature along the flow path, but the average surface temperature is higher in the case with SS pipes, see Fig. 2, due to their additional thermal resistance. On the contrary, the two peak temperatures on the tile surface are
Fig. 2. Temperature map (◦ C) of the tile surface computed without (a) and with (b) thin SS heat pipes embedded in the CuCrZr heat sink, respectively, in the case of uniform surface heat load.
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Fig. 3. (a) Temperature map (◦ C) of the surface of the fluid domain in the inner manifold region, computed in the case with thin SS pipes embedded in the CuCrZr heat sink and uniform surface heat load. (b) Toroidal cross section of the FW06 panel at the level of the inner manifold: material composition from the top (plasma) side: Be tiles (yellow), Cu compliance layer (blue), CuCrZr heat sink (green), stainless steel support (red) also around the inner manifold, and water coolant (cyan). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Table 1 Peak temperature values (◦ C) at different locations, computed without and with thin SS pipes embedded in the CuCrZr heat sink,a in the case of uniform surface heat load. Location
Without thin SS pipes
With thin SS pipes
Tile surface Interface between tiles and Cu layer Interface between Cu and CuCrZr layers SS pipes in CuCrZr sink Water (in the pipes) Water (average on outlet section)
195.1 174.5 172.5 – 131.5 104.7
195.1 172.9 171.3 140.0 128.7 104.4
a
Two different meshes are used in the two cases, see Part I [3].
identical in the two cases, see also Table 1, and this can be understood looking at the location of the peak temperature, which is on the tile(s) close to the panel centerline on top of the inner manifold, see also Fig. 3a below, where the SS pipes are not present. The poor heat removal capability in that region is a combination of the poor flow at that location, see Part I, and of the layer structure of the different materials, with more (poorly conductive) SS and less (highly conductive) CuCrZr below the tiles in that region, see Fig. 3b below. As far as the water temperature is concerned, the peak in the pipes is higher in the case when the thin SS pipes are not included in the model, as expected. Note, however, that when the thin SS pipes are included in the model, the peak water temperature is located in the inner manifold, see Fig. 3a. The computed peak temperature in the Be tiles is well below the acceptable ITER limit of 660 ◦ C. The temperature map computed on the surface of the fluid domain (inlet section + outlet section + walls) using the fine mesh is shown in Fig. 4. The pattern of progressive increase of the temperature while moving along the hydraulic path is clearly observed, except for the peaking of the temperature again in the inner manifold of the central finger, see Fig. 4a. A zoom of the temperature map computed on the inner manifold wall using the fine mesh is shown in Fig. 3. It is seen that the temperature on the second and third manifolds varies by ∼50 ◦ C when going from the region just below the hottest tiles to the SS support on the back of the panel. The shape of these two manifolds, improved in order to reduce the stagnation regions, forbids any sort of mixing between the water in the back and below the tiles. In Fig. 5 we report the temperature map computed on a section cutting the water in the first and third outer manifolds, when the thin SS pipes are included in the model. The effect of the inflow of
Fig. 4. Temperature map (◦ C) of the surface of the fluid domain (inlet + outlet + walls) computed in the case with thin SS pipes embedded in the CuCrZr heat sink and uniform surface heat load: (a) front (plasma side) view; (b) back view.
cold water from the couple of pipes in the CuCrZr sinks is clearly visible, while the surrounding water is hotter due to the direct heating on the manifolds themselves. In view of the relatively low heat conductivity of SS a large temperature difference arises between the outer and inner radius of the SS pipes embedded in the CuCrZr heat sink, which may give rise to non-negligible thermal stress. Our simulations show that the maximum temperature difference occurs in the last finger. On the plasma side of the pipe the temperature varies by ∼10 K on the pipe thickness (0.5 mm), while its variation remains below 5–6 K on the back side, see Fig. 6. As a final remark on the detailed comparison between the temperature maps computed with and without SS pipes embedded in the CuCrZr heat sink, we can state that the results obtained in the two cases are within ∼10% of each other, in terms of temperature increase with respect to the coolant temperature at the inlet. We thus consider the model without SS pipes to be an acceptable
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Fig. 7. Map of the wall heat flux (W/m2 ) to the water coolant, in the case of uniform surface heat load computed including the thin SS pipes in the model.
Fig. 5. Temperature maps (◦ C) on a cross section of the fluid domain in the first (a) and third (b) outer manifold region, computed using the fine mesh in the case of uniform surface heat load.
approximation in the case of uniform surface heat load. It is then justified to use below the similar approximation for the study of the thermal-hydraulic transient in the whole FW06 panel, under uniform surface heat load. 2.1.2. Heat transfer coefficient We now move to the post-processing of the results above in terms of HTC, which is defined as HTC =
Wall heat flux [W/m2 ] (Twall − Tbulk ) [K]
(1)
The wall heat flux to the water is reported in Fig. 7, on a scale from zero to the maximum value of 0.65 MW/m2 , where positive values represent the regions where the water is cooling the structure (in some limited portion of the sides of the boxes of the inner manifolds the water actually heats the solid, not shown, giving rise to a negative heat flux).
As far as the pipes are concerned, it is straightforward to postprocess the computed results evaluating first the average wall heat flux (Fig. 8a), wall temperature and water bulk temperature (Fig. 8b) at selected axial locations along the pipe and then applying (1) to obtain the profile of the HTC along the hydraulic path in each finger (Fig. 8c), to be compared with the results of available correlations (Fig. 8c). In Fig. 8a we note that the peak and average fluxes differ significantly only in the small pipes embedded in the CuCrZr heat sink, as they are most exposed to the one-sided heat flux from the plasma. On the contrary, in the larger pipes embedded in the SS support the wall heat flux is roughly uniform on each cross section thanks to the homogenizing action of heat conduction in the different solid structures. In Fig. 8b we see that the bulk water temperature progressively increases from the inlet to the outlet of the channel. On the other hand, the wall temperature is more sensitive to the location of the pipe with respect to the heated tiles, resulting in two distinct increasing profiles along the small pipes and along the large pipes. In Fig. 8c we see that the HTC coming from the post-processing of the CFD results roughly falls in the range (0.5–1.5) × 104 W/(m2 K) and is typically well (and in any case conservatively) approximated by the HTC coming from the Sieder–Tate correlation [8]. Consistently with the fact that this correlation requires the turbulent flow to be fully developed, we cannot expect it to apply when entry effects are still relevant. The CFD results predict an HTC which is larger than that coming from the correlation due to the presence of swirled flow at the beginning of the pipes, see Fig. 9, which enhances the heat transfer. Deducing an HTC in the case of the inner and outer manifolds is much less straightforward than in the case of the cooling pipes, because of the ambiguity in the definition of the bulk water temperature. If we try to extract a single value of HTC from averaged values of temperature and wall fluxes over each manifold, we find HTC up to several tens of W/(m2 K). On the other hand, if we should use the FLUENT diagnostic for the HTC, which returns the ratio between the wall heat flux and the temperature difference between the wall and the adjacent fluid cell [5], we would find HTC up to several thousands of W/(m2 K). This ambiguity cannot, unfortunately, be easily resolved. 2.2. Peaked surface heat load
Fig. 6. Temperature map (◦ C) on the cross section of an SS pipe (last finger, central location along the finger), in the case of uniform surface heat load.
Also for the case with peaked surface heat load, the simulations have been run both with and without thin SS pipes. However, in view of the fact that the case without SS pipes is mainly relevant for the transient analysis of the entire FW06 panel below, where only the uniform surface heat load case will be considered, we concentrate here on the discussion of the results obtained with SS pipes, unless otherwise noted.
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Fig. 9. Evidence of swirl flow near the entrance of the cooling pipes, from the computed path lines drawn from the fluid inlet and colored by fluid speed, in the case of uniform surface heat load (thin SS pipes included in the model).
peak of the surface heat load is located and on the third (hottest) finger of the hydraulic series, see Fig. 10a, as expected. The temperature gradient across the finger, moving away from the plasma, is significant: ∼180 K across the 1 cm tile thickness (i.e., a comparable gradient to that seen on the thin SS pipes in the uniform surface heat load case), and ∼10 K across the 2 mm Cu layer. The peak surface temperature of the water, again located below the peak surface heat load at the finger knee, see Fig. 10b, is ∼225 ◦ C, which is below the saturation temperature at the operating pressure (∼250 ◦ C). The comparison between peak temperature values in different regions of the FW06 panel, obtained for the peaked surface heat load, without and with thin SS pipes, is reported in Table 2. While obviously the (bulk or average) water temperature is only marginally influenced by the presence of the SS pipes, the peak temperature values on the tiles, Cu compliance layer and CuCrZr sink are dramatically influenced by the neglection of the thermal resistance contributed by the SS pipes. In particular, the peak temperature increase on the tiles is underestimated by ∼50 K when using the coarse grid, although in relative terms this is “only” ∼15% of the total temperature increase of the tiles. It may therefore be concluded that a model neglecting the thin SS pipes should not be fully adequate for the study of the thermal-hydraulic effects of a peaked surface heat load. (The presence of the latter could still be approximately taken into account, even in a model of the whole panel and with a relatively coarse mesh, by introducing an ad hoc thermal resistance between the CuCrZr and the water fluid domain.) In all cases the peak Be temperature is always below the acceptable maximum of 660 ◦ C. We now proceed and evaluate the temperature difference across the thickness of the SS pipes. The hottest point in the SS pipes is located below the surface heat load peak, as expected, see Fig. 11. The maximum temperature difference across the pipes also occurs below the load peak, on the last finger, reaching ∼45 K, see Fig. 11. 2.2.2. HTC and CHF margin Starting from the averaged wall heat flux (not reported here) and from the wall and bulk temperature, suitably averaged over
Fig. 8. Computed profiles along the hydraulic paths in each finger, including the thin SS pipes in the model, in the case of uniform surface heat load. (a) Wall heat flux: average (solid), peak (dashed). (b) Wall temperature (solid), bulk water temperature (dashed). (c) HTC: from the post-processing of the CFD simulation (solid), from the Sieder–Tate correlation (dashed).
2.2.1. Temperature maps The temperature maps computed on the tile surface and on the surface of the fluid domain are shown in Fig. 10. The peak temperature value on the channel is reached on the tiles where the toroidal
Table 2 Peak temperature values (◦ C) at different locations, computed without and with thin SS pipes embedded in the CuCrZr heat sink,a in the case of peaked surface heat load. Location
Without thin SS pipes
With thin SS pipes
Tile surface Interface between tiles and Cu layer Interface between Cu and CuCrZr layers SS pipes in CuCrZr sink Water (in the pipes) Water (average on outlet section)
443.3 267.3 256.1 – 223.7 127.2
492.7 310.7 300.7 269.8 228.5 127.2
a
Two different meshes are used in the two cases, see Part I [3].
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Fig. 10. Temperature maps (◦ C) computed including the thin SS pipes in the model, in the case of peaked surface heat load: (a) tile surface; (b) water surface.
The critical heat flux (CHF) margin has been evaluated starting from the definition of CHF at the fluid wall, which can be evaluated from the simulation results following the definitions given in [9]. The CHF margin (CHFM) has been computed at each selected section, for the sink pipes as well as for the SS support pipes, as CHFM =
CHF Wall Heat Flux
(2)
For the denominator of (2), the peak heat flux at the selected section was considered. The resulting distribution of the CHFM in the case of the peaked surface heat load is reported in Fig. 12c. The CHFM decreases where the surface heat load peaks, and the minimum value (computed adopting in (2) the peak wall heat flux) is ∼5.7, which is well above the design requirement of 1.4 retained in the BM. 3. Whole-panel transient thermal-hydraulic analysis Fig. 11. Temperature map (◦ C) in the thin SS pipe thickness (last finger, central location along the finger), in the case of peaked surface heat load.
the perimeter and cross section, respectively (see Fig. 12a), the HTC has been computed from (1) and is reported in Fig. 12b. The temperature profile along each portion of the different fingers clearly keeps memory of the localized surface heating, showing a peak below the location of the surface load peak, even on the back side (SS support pipes), see Fig. 12a. The computed HTC is again on average well approximated by the HTC derived using the Sieder–Tate correlation, see Fig. 12b – the enhancement of the HTC due to the flow swirl is visible also in this case. It is also interesting to note that the value of the HTC is not very different from what obtained above in the case of uniform surface heat flux, which confirms the correctness of the recipe at least in a case like the present one, where the heating does not determine a dramatic change in the flow field driven by the pumps.
We analyze here the thermal-hydraulic response of the whole FW06 panel, when subject to the transient heat load scenario, corresponding to a standard plasma pulse, as presented in Part I. The surface heat load is assumed to be uniform and reaches 0.35 MW/m2 during the flat top. A series of pulses is analyzed to check the achievement of a periodic thermal-hydraulic response of the panel as well as of possible steady-state conditions during each pulse. The mass flow rate distribution among the different channels shows a limited non-uniformity similar to what obtained in the pure hydraulic simulations [3], consistent with the fact that the uniform heat load (surface + nuclear) cannot significantly affect the flow pattern in the FW06 panel. The temperature evolution in the different solid materials and in the coolant is computed and reported below. A sensitivity study on the time stepping and on the selected solution algorithm shows that the computed temperature maps are reliable within few percent in the worst case, see Appendix B.
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Fig. 13. Evolution of different variables during the first 13 plasma pulses: (a) Water outlet temperature (◦ C); (b) Max water temperature (red dashed), max Inconel temperature (blue solid), average SS temperature (◦ C) at SOB (triangles) and at EOB (circles). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 12. Computed profiles along the hydraulic paths in each finger, including thin SS pipes in the model, in the peaked surface heat load case: (a) Wall temperature (solid), bulk water temperature (dashed). (b) HTC: from the post-processing of the CFD simulation (solid), from the Sieder–Tate correlation (dashed). (c) CHF margin with respect to the peak heat flux.
3.1. Time evolution The simulation has been run for 13 pulses, starting from the purely hydraulic steady state (no energy equation), see Part 1. The evolution of some of the physical quantities that have been
monitored during the simulation, and namely the water outlet temperature, shown in Fig. 13 a, the water maximum temperatures, the SS average temperature at start of burn (SOB) and end of burn (EOB), shown in Fig. 13b, proves that periodic behavior is reached in most cases already after the 3rd pulse. Only the bolt peak temperature, also shown in Fig. 13b, has not reached a fully periodic behavior yet, although the residual increase of Tpeak in the bolt (∼343 ◦ C at the last EOB) between subsequent pulses is very small. The reason for this behavior is discussed below. The pressure drop across the whole FW06 panel stabilizes during the flat top and dwell periods at ∼0.93 bar after the 3rd pulse. This value is slightly larger than the value obtained in the purely hydraulic study presented in Part I, where the fluid temperature was assumed to be constant and equal to 100 ◦ C (instead of the average ∼80–85 ◦ C found in this case). The evolution of the average temperature of different materials during the 13th pulse is shown in Fig. 14, together with the maximum tile surface temperature. Notice that the SS average temperature is still slightly increasing at the end of the heating phase, driven by the Inconel temperature evolution, which is completely unsteady during the whole duration of the pulse. For the sake of completeness we mention that, in three different regions in the solid computational domain, an oscillatory behavior appears during the heating phase, but disappears as the power
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Fig. 14. Evolution of the average temperature (◦ C) of different materials during the 13th plasma pulse: (a) Cu, CuCrZr, SS, Inconel, water; (b) Be (the maximum tile surface temperature is also shown, solid line).
Fig. 15. Temperature maps (◦ C) at SOB: (a) equatorial cross section of the FW06 panel; (b) equatorial cross section of bolt and washer.
is switched off in the dwell phase. The monitored peak temperature values of Cu, CuCrZr and SS in these regions suffer of this oscillatory behavior, possibly due to small mesh defects, but the oscillations remain localized in a negligible portion of the computational domain for the whole transient. 3.2. SOB We discuss here the computed solution at the end of the 13th pulse. This is at the same time the end of the dwell period and the start of burn (SOB) for the subsequent pulse. Fig. 15a shows that the surface of the tiles is well cooled and returns to its initial temperature (∼70 ◦ C, coincident with the coolant inlet temperature), before the beginning of a new pulse. On the other hand, the bolt turns out to be the worst cooled region, see also the zoom in Fig. 15b. The bolt is heated by the nuclear volumetric heat load and on its top surface it is also subject to the surface heat load. As on the lower part of the panel, including the bolt, an adiabatic BC was (very conservatively) imposed, the bolt can only be cooled by thermal conduction through the washer. (To avoid assuming adiabatic boundary conditions between bolt and SB, one could include in the model the SB insert where the central bolt is screwed in and prescribe there suitable contact heat transfer coefficients [4].) The washer refrigeration is again provided only by conduction through the thin cylindrical wall of the lower part of the I-beam, resulting in quasi-1D temperature profiles in both regions. Since the active cooling is far away from this part of the I-beam, the region of the bolt and washer is not as well cooled as the rest of the panel. The result is that the bolt temperature needs many more pulses than any other region of the FW06 panel to reach a periodic behavior.
Fig. 16. Temperature map (◦ C) on the heated surface of the tiles at SOB (all temperature values above 215 ◦ C are represented as equal to 215 ◦ C in the figure).
Indeed, pulse after pulse the increase of the bolt temperature at periodic conditions of the rest of the I-beam allows increasingly better heat transfer and therefore faster recovery of the conditions at SOB in the bolt, see Fig. 13b.
3.3. EOB We discuss here the computed solution 400 s after the start of the 13th pulse, i.e. at the EOB. The temperature on the heated surface of the tiles is shown in Fig. 16. The repetitive 2D pattern directly reflects the single channel cooling paths.
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Fig. 17. Temperature maps (◦ C) at EOB: (a) equatorial cross section of the FW06 panel (all temperature values above 220 ◦ C are represented as equal to 220 ◦ C in the figure); (b) bolt and washer cross section.
Fig. 17a shows the temperature map on the equatorial cross section of the FW06 panel. The hot spot is again in the bolt, which also drives the local temperature increase in the surrounding stainlesssteel region. The inlet piping is of course always at 70 ◦ C. The detail of the temperature distribution on the bolt cross section is presented in Fig. 17b, where the peak in the lowest region, which is the worst cooled part, is clearly visible. Two other warm regions are identified in the contact zone between the supports and the I-beam, see the red ovals in Fig. 17a, where the local over-heating results from a combination of distance from active cooling regions and adiabatic BC assumed in the simulation on the I-beam back side, notwithstanding the lower heat deposition compared with the tiles. Fig. 18 shows two cross sections of the panel in the (x–z) plane, located in correspondence of the black lines in Fig. 17a, i.e. where the above-mentioned warm regions in the I-beam/support are located. It is clear that on these two cuts the highest temperatures are not reached on the tiles, but rather they are located in the back of the SS supports, in the last finger of each hydraulic channel. In Fig. 18, the cooling path of the water is also clearly visible, getting hotter as it moves downstream in the hydraulic series of the three fingers. The top and bottom maps do not show perfectly symmetric distribution because of the above-mentioned asymmetries in the mass flow rate distribution among the different channels. Notice also the hot spots on the tiles of the side fingers due to the larger distance between tile edge and cooling pipes. Fig. 19 shows the poloidal cross section of the I-beam at the midplane between A and B sides, where the temperature peak of ∼277 ◦ C is clearly visible in the top left corner and due to the ill cooling of that portion of the plate. A comparable hot spot is present in the back part in contact with the bolt.
Fig. 18. Temperature map (◦ C) at EOB on the two poloidal cuts identified by the black segments in Fig. 17: (top) side B; (bottom) side A.
Fig. 19. Temperature map (◦ C) at EOB on a poloidal cross section of the I-beam, at the midplane between side A and side B, excluding the bolt and the water coolant.
The asymmetry of the flow distribution between A and B side of the FW06 panel discussed above, induced by the bending of the inlet pipe, also reflects in an asymmetry of the temperature distribution in the central part of the I-beam and, therefore, in the inlet temperature to the channels, see Fig. 20.
Fig. 20. Temperature profiles (◦ C) at EOB: (a) back side of the fluid domain, including inlet pipe; (b) front (plasma) side of the I-beam, with the small inlet pipes to the different channels in the central part.
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4. Conclusions The comprehensive thermal-hydraulic model of the ITER FW06 panel has been developed within the ANSYS-FLUENT framework. Two problems have been considered: a single cooling channel at steady state, including most of the geometrical details, and a coarser but transient analysis of the whole panel. The main conclusions of the single-channel steady-state thermal-hydraulic analysis are: • If compared with the uniform surface heat load scenario at 0.35 MW/m2 , the case of peaked surface heat load at 2 MW/m2 , always combined with the volumetric nuclear heat load, leads as expected to more severe conditions for the FW06 panel: ◦ The temperature on the surface of the tiles reaches a maximum of ∼493 ◦ C (vs. ∼195 ◦ C in the uniform surface heat load case), which is however still well below the recommended maximum of 660 ◦ C. ◦ The temperature in the CuCrZr reaches a maximum of ∼300 ◦ C, which is below the recommended maximum value of 350 ◦ C. ◦ The maximum temperature difference across the thin stainless steel wall of the pipes embedded in the CuCrZr heat sink peaks at ∼45 K, vs. ∼10 K peak in the uniform surface heat load case. ◦ The minimum critical heat flux margin is ∼5 (vs. ∼30 in the uniform surface heat load case), which is however still well above the acceptable minimum of 1.4. • The heat transfer coefficient between water coolant and stainless steel pipes, at ∼(0.5–1.5) × 104 W/(m2 K), is well approximated by the Sieder–Tate correlation in the fully developed flow regions of the cooling pipes, while it further increases near the entrance of the pipes due to swirl flow effects. This result is independent of the surface heat load profile. • In the case of uniform surface heat load, neglecting the thin SS pipes in the model, as it is needed to do for the transient thermalhydraulic study of the entire FW06 panel, gives results which are reasonably close to those obtained including the thin SS pipes. In the case of peaked surface heat load, the two models give very different results. The main conclusions of the whole-panel transient thermalhydraulic analysis under uniform surface heat load are: • The thermal-hydraulic conditions in the FW06 panel become periodic after three pulses except for the bolt, whose peak temperature after 13 pulses is still slightly increasing, partly due to the (conservative) boundary conditions assumed in this study. The bolt temperature is also the only quantity of interest that does not reach a steady state during the pulse flat top • The following peak temperatures have been computed at EOB: ◦ ∼200 ◦ C on the tiles, well below the recommended limit of 660 ◦ C for Be; ◦ ∼170 ◦ C on the CuCrZr, well below the recommended limit of ∼350 ◦ C for this material; ◦ ∼280 ◦ C in a portion of the I-beam surface directly exposed to the plasma and poorly cooled, but still well below the recommended limit of 450 ◦ C for the stainless steel; ◦ ∼343 ◦ C in the Inconel (bolt and washer), which is the peak temperature in the whole FW06 panel, at the 13th pulse EOB (still slightly increasing). • The whole-panel (coarse mesh) transient results at EOB are in substantial agreement with the outcome of the fine-mesh single-channel steady-state analysis, in terms of tile temperature, as well as of HTC and CHF margin, thanks to the fact
that all of the relevant quantities (except the bolt and washer peak temperature, however obviously not included in the singlechannel analysis) reach a steady state during the pulse flat top. Acknowledgments The work at Politecnico di Torino was partially financially supported by F4E under contract F4E-2009-OPE-031-01-03. We thank F. Subba for implementing in FLUENT the routine for the nuclear heat load. We also thank an anonymous reviewer for several comments which led to an improvement of the quality of the paper. Appendix A. Whole-panel steady-state analysis The single-channel steady-state analysis presented above did not include the I-beam and assumed an adiabatic BC on the back of the SS support. In order to assess the adequacy of that assumption, which was needed due to the dramatic simplification of the computational domain with respect to the whole FW06 panel, we present here a few results of a whole-panel steady state analysis. Starting from the same pure hydraulic steady state condition adopted as initial condition for the whole-panel transient study, a steady state run is performed, with the nuclear + uniform surface heat load set constant at the flat top level. The following results refer to the solution obtained after 450 iterations. Fig. 21 contains a comparison of the temperature map computed on the heated surfaces of the tiles in three different cases: (a) the coarse-mesh steady-state single-channel computation presented in Section 2, (b) the whole-panel steady-state computation and (c) the whole-panel transient computation (results at EOB) presented in Section 3. The agreement between the three is shown to be excellent, giving a good indication of the adequacy of the single-channel boundary condition on the back of the SS support. The steady-state analysis of the whole panel allows computing the heat transfer between the support and the I-beam, which was neglected in the single-channel study. Referring to a single channel, it turns out that ∼1 kW goes from the I-beam to the support, which is small if compared with the ∼29 kW from the plasma onto the tile surfaces, on top of the ∼18 kW nuclear heat load. The adiabatic
Fig. 21. Temperature maps (◦ C) on the heated surface of the tiles of channel C13 (see part I [3]): (a) from the single-channel coarse-mesh computation presented in Section 2; (b) from the steady-state computation on the whole panel; (c) from the EOB solution of the whole-panel transient computation presented in Section 3.
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Appendix B. Numerical sensitivity study on the whole-panel transient results In order to assess the dependence of the presented results on different numerical parameters used for the transient simulation of the whole FW06 panel, a sensitivity study has been carried out. The values of four different variables, i.e. the maximum Inconel temperature increase (the most sensitive parameter), the outlet water temperature increase, the maximum water temperature increase and the water pressure drop, have been computed at the EOB of the first plasma pulse (t = 400 s) and the relative difference with respect to the maximum increase of that variable has been evaluated. Fig. 22a shows the sensitivity analysis with respect to the time step adopted. If compared with the solution obtained with the most refined discretization (t = 1 s), the relative error in the case of t = 5 s (which is the time step used for the analysis presented in Section 3) is within ∼4%. Concerning the maximum number of iterations per time step, Maxiter , Fig. 22b shows that the relative error in our results above (obtained with Maxiter = 5), with respect to the solution obtained with Maxiter = 20, is always within ∼4%. Concerning the choice of the numerical scheme, Fig. 22c shows that if we use the coupled pressure–velocity algorithm instead of the segregated scheme used above, or if we use the second order time scheme instead of the first order used above, the differences arising in the solution are always within 1.5%. Also the possible effect of the introduction of the acceleration of gravity has been checked, but the effect is shown to be negligible, as expected considering the relatively small temperature differences in the water and the fact that the flow direction is mainly toroidal (i.e., at constant height). References
Fig. 22. Results of the sensitivity analysis on the whole-panel transient thermalhydraulic solution: (a) relative error in different variables with respect to the results obtained with time step t = 1 s. (b) Relative error in different variables with respect to the results obtained with maximum 20 iterations per time step (c) Relative difference in different variables with respect to the results of the scheme adopted above (segregated + 1st order in time + no gravity).
assumption on the back of the SS support, adopted for the singlechannel computations in Section 2, can therefore be considered acceptable, with an error of a few %.
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