Detailed electromagnetic numerical evaluation of eddy currents induced by toroidal and poloidal magnetic field variation and halo currents

Fusion Engineering and Design 83 (2008) 1625–1630

Contents lists available at ScienceDirect

Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes

Detailed electromagnetic numerical evaluation of eddy currents induced by toroidal and poloidal magnetic field variation and halo currents M. Roccella a,∗ , A. Marin a , F. Lucca a , M. Merola b a b

L.T. Calcoli S.a.S. Piazza Prinetti, 26/B, Merate (Lecco), Italy ITER Team, Cadarache, France

a r t i c l e

i n f o

Article history: Available online 29 August 2008 Keywords: Divertor EM loads Halo currents Thermal quench

a b s t r a c t A detailed evaluation of the EM loads in the ITER divertor during plasma disruptions is mandatory for the correct dimensioning of the divertor component. The EM loads during plasma disruptions are mainly produced by: (1) toroidal flux variation (TFV) during the thermal quench (TQ) and current quench (CQ); (2) halo currents (HC); and (3) poloidal flux variation (PFV) during TQ and CQ phase. The new ITER reference disruption and the last changes in the divertor design have been considered in the EM models created to calculate all the EM loads due to TFV, HC and PFV. All the analyses have been performed for the three different main design options of the divertor plasma facing units (PFU). The effects of PFV have been analyzed using an EM-zooming procedure that has allowed a good detail of the component model, while new numerical approaches have been developed for the evaluation of the effects due to TFV and HC maintaining the same detail for the divertor model. Separate models have been developed to evaluate the equivalent electrical resistivities of the various PFU options; this allows in the full 3D model a strong simplification of a geometry which would otherwise be very complex. The effect of an electrical surface bridging of the PFU castellation has also been taken into account. © 2008 Elsevier B.V. All rights reserved.

1. Introduction The three main sources of EM loads on the in-vessel components during plasma disruptions are: the TFV during the TQ and CQ, the HC during the CQ and the PFV during the TQ and CQ. The currents induced by TFV and HC are mainly poloidal currents; in the divertor the interaction of these currents with the toroidal magnetic field produces a traction force during the TQ (pulling the component toward the plasma) and a pressure force during the HC and the CQ phase (pushing the component against the vessel). These are in plane forces; out of plane forces could be even generated by the misalignment between these poloidal currents and the poloidal magnetic field. By performing three different analyses for the TFV, HC and PFV, it has been shown that, as expected, the out of plane forces induced by TFV and HC have a very minor effect with respect to the out plane forces coming from PFV (via interaction with the toroidal magnetic field). The three EM analyses (TFV, HC and PFV) need different boundary conditions and different kinds of excitations: orthogonal field

∗ Corresponding author. Tel.: +39 039 9285005/06 9413067; fax: +39 039 5984000. E-mail address: [email protected] (M. Roccella). 0920-3796/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2008.07.013

at the boundary and poloidal excitation currents for TFV and the HC; tangent field at the boundary and toroidal excitation currents for the PFV; furthermore the PFV and the TFV problems are at “imposed induced voltage”, while the HC problem is at “imposed current”. Due to these facts, to take the maximum advantage of the component symmetries, the three EM analyses have been performed using three different EM models, which have the same divertor mesh, while the mesh surrounding the divertor component has been changed according to the three different boundaries and excitation conditions. In this way the various EM contributions have been easily added, element by element, in the post-processing phase and the resultant force has been provided as input for the related structural analyses. The activity described in this article has been performed in the frame of an EFDA contract [1]. It consists of the EM analyses of three fast vertical displacement events (VDE): (1) the fast downward VDE of type II with a 36 ms duration linear current quench (LCQ); (2) the fast downward VDE of type II with exponential current quench (ECQ) characterised by 16 ms time constant; and (3) the fast downward VDE of type III with 36msLCQ. The numerical simulations of these events have been provided by ITER and they will be here in after labelled VDEII 33msLCQ, VDEII 16msECQ and VDEIII 36msLCQ respectively. Three different PFU design options (Table 1) for the inboard and outboard vertical targets have been

1626

M. Roccella et al. / Fusion Engineering and Design 83 (2008) 1625–1630

Fig. 1. (a) Finite element model of PFU option 3 for the calculus of equivalent resistivity. The lower PFU differs from the upper PFU only for the swirling tape inside the Cu pipe. (b) Drawing of VT with the PFU details. In the straight part of the VT a swirling tape is placed inside the Cu pipe. (c) Circuital loading schema for poloidal and toroidal W bridging. (For interpretation of the references to color in the artwork, the reader is referred to the web version of the article.)

M. Roccella et al. / Fusion Engineering and Design 83 (2008) 1625–1630

1627

Table 1 Poloidal and toroidal electrical resistivities for the three PFU options and the Dome assuming poloidal and toroidal bridging pol (␮ m)

tor (␮ m)

Option1 up

0.0364

Option1 dw Option2 up

0.371 0.188

∞ 0.517

0.544

Option2 dw Option3 up

0.371 0.188

∞ 0.517

Option3 dw Dome

0.177 0.089

0.516 0.419

considered—option 1: W tiles + CuZr poloidal bar in the upper part of the vertical targets and C mono-blocks in their lower part; option 2: W mono-blocks (upper) and C mono-blocks (lower); option 3: W mono-blocks (upper) and W mono-blocks (lower). For all the three options an electrical toroidal and poloidal bridging produced by 1 mm W melting has been considered. All the EM analyses have been performed using ANSYS code. In the following sections it will be reported: in Section 1 computation of the equivalent electrical resistivities for the three PFU options and for the Dome. In Section 2 main characteristics of disruption events used for the analyses. In Sections 3 and 4 description of the models used for the EM analyses for PFV, TFV and HC and main results. 2. Equivalent electrical resistivities for the PFU and the Dome The various PFU targets and the Dome tops are made of linear finite elements in poloidal direction, about 4 cm wide in toroidal direction. The equivalent electrical resistivities of the different design options of these elements have been calculated performing separate detailed EM analyses on a single element modulus reproducing in full detail their complex features. The model used for the option 3 is shown in Fig. 1 and it has been derived from the Vertical Target drawings as reported in Fig. 1b. A linear current ramp I(t) has been imposed to a sample of length L and the resulting voltage drop V(t) at the sample ends V (t) =

∂A × L + R(t) × I(t) ∂t

(1)

has been evaluated by the code; the first term, including the time derivative of potential vector A, is constant in time for a linear current ramp. The current ramp has been applied (to the copper tube for poloidal bridging and to the W melted region for toroidal bridging) combining an electric circuit to the mesh as reported in Fig. 1c. The results of the analyses show that the resistance R(t) reaches its saturation value after about 1 ms for all the samples. This means that for the time scales of EM transients produced by ITER disruptions, a constant in time equivalent electrical resistivity can be used. In Table 1 the saturated equivalent orthotropic resistivities are given, for the PFU and the Dome, in case of electrical poloidal and toroidal bridging. In the 3D analyses for the target PFUs and the Dome, orthotropic material properties have been used. 3. The excitations In Fig. 2 the plasma configuration/parameters vs. time are shown for VDEII 36msLCQ, VDEII 16msECQ and VDEIII 36msLCQ. In Fig. 2b and c the time behavior of TFV and HC for the three disruptions is shown. The main difference between VDEII and VDEIII is the time at which the TQ occurs during the VDE. During the VDEIII, the TQ and

Fig. 2. Behavior of plasma main parameters vs. time (s); (a) plasma current and position, (b) TFV, and (c) HC. The starting time of the VDEs has been shifted to have the TQ at the same time. (For interpretation of the references to color in the artwork, the reader is referred to the web version of the article.)

the onset of HC take place somewhat later with respect to VDEII, when the plasma is smaller and nearer to the divertor. This fact implies for VDEIII a higher HC and a higher EM loads induced by PFV; on the other hand, due to the delayed TQ, some plasma energy loss occurs during the slow phase reducing the toroidal field drop at the TQ. 4. EM analyses of PFV (the zooming approach) The plasma disruption simulation provides as output current filaments in the plasma region, whose number and position, vary with time. This fact would require a mesh change at each time step.

1628

M. Roccella et al. / Fusion Engineering and Design 83 (2008) 1625–1630

Fig. 3. Field modulus vs. time in selected points internal to the zoomed region. Comparison between the field produced directly by the DINA excitations and the field reproduced by the zooming excitations. The maximum error in this example is within 1%, while the maximum error in the region is below 3%. (For interpretation of the references to color in the artwork, the reader is referred to the web version of the article.)

In any case, due to the very high number of filaments needed for the event description, a very fine mesh of the plasma region should be necessary even in case of filaments at rest. Furthermore to take into account the long range effects produced by far conductors the whole region of the EM transient should be modelled with enough detail. Fortunately, this last effect is usually axis symmetric and can be reproduced by axis symmetric excitations surrounding a region (the zoomed region) including the components of interest. The currents in the conductors (used as excitations in the zooming technique) surrounding the zoomed region have been calculated and the magnetic field by the zooming technique and DINA [2] has been compared and reported in Fig. 3. The model used for the PFV analysis is shown in Fig. 4. To reproduce the real ITER toroidal periodicity the finite element model consists of a detailed mesh of half divertor (3.3◦ ), where the EM loads have been calculated, and of a coarse mesh of the whole adjacent divertor (6.6◦ ). In this way the model includes half of blanket module #1 and the whole module #17. The coarse mesh dif-

Fig. 4. Model used for PFV analyses. The blue elements surrounding the zoomed region represent the toroidal excitations of the 3D model and correspond to the zooming excitations reported in Fig. 3. (For interpretation of the references to color in the artwork, the reader is referred to the web version of the article.)

Fig. 5. Model used for the TFV EM analyses. The poloidal excitations reproduce the same toroidal flux variation of the plasma during TQ and CQ. (For interpretation of the references to color in the artwork, the reader is referred to the web version of the article.)

fers from the detailed one only in the element number in toroidal direction, being the element number in the other directions the same. The same orthotropic material properties have been used for the PFU and the Dome top part in the coarse and detailed meshes, while for the other conducting parts of the coarse mesh

Fig. 6. Model used for the EM analyses of HC. The input and output of HC and the correspondent current fraction are in blue and red respectively. (For interpretation of the references to color in the figure legend, the reader is referred to the web version of the article.)

M. Roccella et al. / Fusion Engineering and Design 83 (2008) 1625–1630

1629

Fig. 7. The finite element model of the divertor used for PFV, TFV and HC EM analyses. (For interpretation of the references to color in the artwork, the reader is referred to the web version of the article.)

a volume averaged material properties equal to the ones of the detailed mesh have been used. The mesh reproduces in fine detail the real geometry of the divertor; thus, except for the PFU and the Dome top part, no equivalent resistivities have been calculated. The models used for the TFV and HC analyses are shown in Figs. 5 and 6. The models are composed by 8-node elements: the divertor is always discretized with 13,000 elements, while the surrounding mesh depends on the case being analysed. As an example, in the TQ analysis, the VV, the excitation and the surrounding

air have been modelled with 2400, 250 and 40,000 elements respectively. Following the ITER prescription, the time behavior of HC was assumed from DINA Output supplied by EFDA, while the input and output positions of the HC was assumed according to the ITER recommendations: the input was 100% at the inboard target, while the output was shared between the Dome top (67%) and the outboard vessel (33%). For the PFV, TFV and HC EM analyses the detailed half divertor model, where the EM loads have been calculated was the same

Fig. 8. The EM loads induced by PFV + TFV + HC on the whole divertor by VDEII36msLCQ and by VDEII16msECQ. The moments reported in (a) and (c) are calculated with respect to the origin of the local system. The x-, y-, and z-axes are in radial, toroidal and vertical direction respectively. (For interpretation of the references to color in the artwork, the reader is referred to the web version of the article.)

1630

M. Roccella et al. / Fusion Engineering and Design 83 (2008) 1625–1630

Table 2 Summary table of EM loads on the whole divertor VDEE 36msLCQ (MN)

VDEII 16msECQ (MN)

Fx

−0.50 (0.13)

−0.45 (0.45)

−0.775 (0.2)

Fy Fz

0.35 (−0.075) −0.62 (0.45)

0.16 (−0.05) −0.625 (0.45)

0.5 (0.23) −0.8 5 (0.2)

Mx My Mz

YDEIE 36msLCQ (MN)

VDEE 36msLCQ (MN*m)

VDEII 16msECQ (MN*m)

YDEIE 36msLCQ (MN*m)

−0.22 (0.08) 0.15 (−0.16) −1.15 (0.45)

−0.21 (0.05:0.05) 0.15 (−0.16:0.0) −0.88 (0.5:0.8)

−0.3 (<0.01) 0.2 (<0.01) −2.4 (1.05)

In parentheses the peak at the TQ time. The second value in parentheses, if present, refers to the fast z drop time.

(Fig. 7). The fields and currents from the different analyses have been added element by element, and the resultant EM loads calculated in the post-processing phase. 5. Main results of the EM analyses In Fig. 8 the resultant loads on the divertor are shown vs. time for the two disruptions VDEII36msLCQ and VDEII16msECQ. These loads include the cumulative effects of PFV, TFV and HC. Looking at the resultant loads the LCQ seems much more severe than the ECQ but considering their time behavior it can be noted that the ECQ shows a much less regular behavior than the LCQ. In particular from the dynamic structural analysis of the divertor presented in the paper “Design Analysis of the ITER Divertor” [3] the very fast positive peak of the moment (Fig. 8c) due to the fast z drop occurring during the ECQ some ms after the TQ (Fig. 2a) produces the highest stress conditions for the attachments between the cassette body and the targets. On the other hand, this peculiar behavior of plasma

movement has not been observed in other similar disruptions; in particular it does not occur during the VDEIII 16ms ECQ. Due to this fact only the analyses of the LCQ have been performed for the VDEIII. In Table 2 the summary of the EM loads for all three disruptions is presented. Summarizing the results of all the three cases it can be stated that: the Mx and Mz moment components and the out plane force Fy are almost completely determined by the eddy currents induced by PFV, while the in plane forces Fx and Fz are almost completely determined by the HC and by TFV. References [1] Study Contract no. FU06-CT-2005-000068 (EFDA 05-985)—Analysis of the revised ITER Divertor design. [2] M. Sugihara, DINA Results/Model 2006, ITER-IDM. [3] G. Samuelli, G. Samuelli, A. Marin, M. Roccella, F. Lucca, M. Merola, B. Riccardi, L. Petrizzi, R. Villari, et al., Design Analysis of the ITER Divertor. Poster Session 1—Poster number 308, in: International Symposium on Fusion Nuclear Technology, Heidelberg, Germany, September 30–October 5, 2007.