ARIES-RS divertor system selection and analysis

Transcription

1 Fusion Engineering and Design 38 (1997) ARIES-RS divertor system selection and analysis C.P.C. Wong a, *, E. Chin a, T.W. Petrie a, E.E. Reis a, M. Tillack b, X. Wang b, I. Sviatoslavsky c, S. Malang d, D.K. Sze e a General Atomics, San Diego, CA, USA b Uni ersity of California, San Diego, La Jolla, CA, USA c Uni ersity of Wisconsin, Madison, WI, USA d Forschungszentrum Karlsruhe GmbH, Karlsruhe, Germany e Argonne National Laboratory, Argonne, IL, USA Abstract The ARIES-RS divertor system is selected and analyzed. A radiative divertor approach using Ne as the radiator is chosen to reduce the maximum heat flux to 6 MWm 2. A 2 mm W layer is used to withstand surface erosion allowing a design life close to 3 full-power-years. This W coating on the V-alloy structure is castellated to meet structural design limits. A detailed description of the calculated heat flux distribution, thermal-hydraulics, structural analysis, fabrication methods and vacuum system design are presented. An innovative design using adjustable bolts is utilized to support the divertor plates, withstand disruption loads and allow adjustment of alignment between plates. With the exception of the concentration of Ne at the divertor, it is found that this divertor system design can satisfy all the design criteria and most of the functional requirements specified by the project Elsevier Science S.A. Keywords: ARIES-RS; Divertor system; Neon 1. Introduction Power exhaust and particle handling are two of the most difficult design problems for magnetic toroidal devices. The peak surface heat flux and target plate erosion rate are primary concerns, followed by the control of impurities and helium ash removal. For the ARIES-RS design, a doublenull divertor configuration creates a practical means to enhance ash removal and pumping while * Corresponding author. focusing the flow of power to the divertor plates. Functional design requirements were established before the initiation of the detailed design. In steady-state conditions, the total heat flux to the vacuum chamber wall must equal the fusiongenerated alpha particle power plus contributions from external power sources such as current drive. Migration of power from the core through the plasma mantle and the scrape-off layer (SOL) and into the divertor region must be taken into account. Robust engineering systems must be designed to remove this power while maintaining high coolant power conversion efficiency /97/$ Elsevier Science S.A. All rights reserved. PII S (97)

2 116 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Scaling Tokamak experimental results of DIII- D [1] to the size and power flux of ARIES-RS, the divertor maximum heat flux is estimated to be much higher than the design goal of 5 MW m 2. Using Ne as the radiating impurity, and by assuming a Ne enrichment factor of 8 at the divertor, the maximum heat flux is reduced to 6 MW m 2. Present experiments have shown an enrichment factor of 3. Possible radiative divertor operation for higher Ne enrichment will have to be demonstrated. However, the required enrichment of eight can also be reduced by increasing the edge density and by increasing the core radiation. These approaches will have to be demonstrated by future experiments. To extend the component life-time a tungsten coating on the V-alloy structure is used to minimize the impact of surface erosion due to interaction with high energy particles. Engineering design including thermal hydraulics and structural analysis on the heat removal component, and the vacuum system are evaluated. Two options for the fabrication of the divertor are also suggested. An innovative support system using adjustable bolts is used to support the divertor plates and to withstand disruption loads. This ARIES-RS divertor design can meet all the fundamental engineering design criteria and material design limits. Details are presented in this paper. 2. Functional requirements The ARIES-RS fusion power plant design are guided by a set of top-level design requirements. Based on these top-level design requirements functional requirements are also prepared for different sub-systems. The list for the divertor system is the following. The divertor system will provide the required exhaust of energy and particles from the scrape-off-layer (SOL). The divertor system will limit impurity influx to the core to levels compatible with the specified plasma confinement mode and performance. The divertor system will limit steady state and transient particle and heat flux to selected invessel components to levels consistent with engineering design requirements. This implies all the material temperature and structural design limits will be met while maintaining high coolant power conversion efficiency. Based on past design experience, the maximum steadystate heat flux design goal is 5 MW m 2.To match the fusion power core components lifetime requirements, the divertor system is designed to a lifetime of 3 full-power-years. The divertor system will provide limiting surface(s) at specified locations for the purpose of plasma start-up and shut-down. The divertor system will withstand thermal and electro-mechanical loads due to one full power disruption per year. The divertor system will withstand the effects of anticipated transient loads, e.g. ELMs and sawteeth, at appropriate frequencies. The divertor system will be confined to space envelopes as defined by the overall configuration and maintenance approach. For maintenance, the divertor module is part of the blanket sector and can only be replaced in the hot cell when the blanket sector is removed from the fusion power core. The divertor system will satisfy all applicable reliability, availability, maintainability, and inspectability (RAMI) requirements. The divertor system will satisfy all applicable interface requirements with other fusion power core systems, including shielding, vacuum, and heat transport systems. The divertor system will accommodate necessary instrumentation and control systems. 3. Initial peak heat flux estimation The ARIES-RS divertor design has a maximum surface heat flux design goal of 5 MW m 2. This value is selected for maximum heat removal while satisfying material design limits. This section presents the first step in the estimation of the maximum surface heat flux at the outboard divertor plate by scaling from Tokamak experimental re-

3 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Table 1 Divertor parameters and estimated maximum heat flux Fig. 1. ARIES-RS blanket/shield and divertor sector. sults to the size and power flux of the ARIES-RS design. The estimated result shows the necessity of distributing the transported power to as large a surface area as possible and leads to the selection of the radiative divertor approach. The ARIES-RS blanket, shield and double-null divertor sector is shown in Fig. 1. A sketch of the fusion core sector cross-section is shown in Fig. 2. The transfer of transported power is followed from the plasma core to the inboard and outboard scrape-off-layers, and then to the collector plates at the divertor in concert with the separatrix geometry. A relatively deep outboard slot ( 1 m), allowing radial transport into the private flux region below the X-point, is used to help trap neutrals and to reduce electron temperature and Major radius (m) 5.52 Minor radius (m) 1.38 Aspect ratio 4 Vertical elongation (X-point) 1.89 Fusion power (MW) 2167 Alpha power (MW) Current drive power (MW) 80.8 Transport power (MW) Core radiation fraction ( f c ) 0.35 Up and dow split 1:1 Outboard and inboard split 4:1 Lower/outboard P SOL (MW) 133 Midplane heat flux SOL thickness (cm) 1 SOL flux expansion 3 Target plate inclination angle 15 l d, divertor footprint width (m) Strikepoint R S (m) 5.07 Outer separatrix radiation correction Q peak (MW m 2 ) sputtering at the target plate. The divertor geometry and estimated transported power distribution parameters for the ARIES-RS design are summarized in Table 1. The ARIES-RS outboard divertor plate peak heat flux is estimated by considering the net power reaching the plate with significant fraction of power, f c, already lost by radiation in the core as shown in Table 1. In this estimation, the expected bremsstrahlung and line radiation losses in the core, and the up/down and inboard/outboard distributions of scrape-off layer power flow are consistent with the experimental database from ASDEX, PDX and DIII-D double-null operation [1]. The in/out power balance at the divertor is consistent with the single-null ELMing H-mode results from DIII-D [2]. The lower/outboard divertor peak target plate surface heat flux is given by: Q peak =0.7P SOL /2 R S l d, Fig. 2. ARIES-RS sector cross-sectional view. where P SOL is the transported power reaching the lower/outboard divertor, R S is the radius at the strike point, l d is the width of the target heat flux foot print on the target (taking into consideration the midplane SOL width, l d of 1 cm, SOL flux expansion of 3 at the divertor and an inclination

4 118 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) of the target plate at 15 ), and the correction factor of 0.7 represents the power distribution between the regions outside and inside of the outboard separatrix. Table 1 shows that the estimated peak heat flux is 25.2 MW m 2 which is very much above our design goal of 5 MW m 2. It does not appear possible to meet this goal by further expansion of the surface area around the strike point. The approach of radiative divertor to reduce the peak heat flux is proposed and presented in the next section. 4. Radiative divertor To reduce the maximum divertor surface heat flux, the power flow into the SOL will need to be dispersed over a wide area of the plasma facing surfaces. One option is by enhancing the radiated power from the divertor and the main plasma, often referred to as radiating divertor and radiating mantle methods, respectively. In the former, excessive power flowing into the divertors is dissipated largely by radiating it away to adjacent divertor surfaces. In the latter, this power flow is radiatively dissipated at the edge of the main plasma before it passes into the SOL. While both methods had their attractive elements, we settled on the radiating divertor approach, since it was more consistent with the ARIES-RS core physics design. A relatively simple accounting of the transported power from the burning core into the SOL and onto the divertor floor, consistent with a peak transport power flux to the floor of 4 MW m 2, allows a determination of the required enhanced radiated power by the addition of an impurity such as Ne or Ar. A simple model of the SOL and divertor plasma was used to determine the plasma density and temperature distributions. Coronal equilibrium radiation rates were used to estimate the impurity radiation. (Details of the divertor physics analysis is presented in the corresponding paper presenting the physics analysis of the ARIES-RS design [3].) The resulting radiated power and heat flux distributions, presented in [3], were used in evaluating the cooling requirements for the plasma facing components. This study shows that adding neon to the plasma system, under conditions consistent with present ARIES- RS design parameters, would radiate a sufficient amount of power in the SOL and divertor regions. The helium concentration is taken as 18% of the plasma ion density. The neon concentration in the core is 0.55%. These are consistent with the core boundary conditions of Z eff =1.7 and an edge density of m 3, but it is found that a divertor impurity enrichment factor (ratio of divertor-to-core impurity concentration) of 8 is required. Such a high enrichment factor is far beyond the present data base of 3. This enrichment factor can possibly be reduced by increasing the edge density and concomitantly increasing the core radiation. Further experimental studies are needed in this area of radiative divertor design. 5. Divertor plasma facing materials For the selection of ARIES-RS divertor plasma facing material, our functional goal is to achieve the same 3 full-power-year lifetime as the fusion power core components. Under steady state operation, when high incident particle and heat fluxes are expected, surface material erosion will have two major impacts to the power plant design. The first is the potential transport of the eroded material into the core, with the possible increase of Z eff and radiation and therefore reduction of the plasma core performance. The second is the limitation of divertor lifetime due to the erosion of its plasma facing surface. Therefore, it is very important to select the suitable plasma facing material. The phenomenon of material erosion is a complex process involving: gross material losses due to physical and chemical sputtering, sublimation and evaporation, redeposition due to plasma transport of ions back to the surface, and surface material interaction with plasma contaminants. The material re-deposition fraction at the divertor can be expected to be quite high, however, high power flux due to transient events such as edge localized modes (ELMs), disruptions and arcing may enhance sputtering erosion and cause surface melting and bulk material transport. These phenomena will also have significant impact on the

5 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) lifetime of plasma facing components. Therefore, in order to understand material erosion at the divertor, it is important to obtain net and gross erosion data in Tokamak devices under different regimes of operation in addition to dedicated sputtering yield experiments. Carbon, beryllium, and tungsten have been considered as the plasma facing material for the ITER-EDA design [4] and V-alloy is the selected structural material for the ARIES-RS design. For these materials much of the erosion yield results were obtained from dedicated sputtering yield experiments. There are very few dedicated Tokamak divertor material erosion experiments except the Divertor Material Evaluation Study (DiMES) at DIII-D [5]. Under similar diverted plasma conditions, the erosion rate of C, Be, V and W are measured after exposure to the divertor strike point at the DIII-D divertor. The relative erosion rates for C, Be, V and W are 4.0, 0.9, 0.5, and 0.1 nm s 1, respectively. Since the DIII-D vacuum chamber is about 90% covered by graphite tiles, the plasma has a carbon background. The metallic samples used for the DiMES experiments are very small, therefore, these measurements represent gross erosion rates while operating with a background of carbon. These materials were exposed to an ion temperature of ev, an ion flux of m 2 s 1, and a heat flux range of about 0.7 MW m 2. It is clear that when extrapolated to the operating condition of the ARIES- RS divertor design, with the possible exception of W, these erosion rates are unacceptably high and will not meet the lifetime goal of 3 years while retaining the material layer to be reasonably thin to meet respective temperature limits. For example, based on the above erosion rates, for a coating thickness of 2 mm, the corresponding lifetime for C, Be, V and W are 139, 617, 1112, and 5560 h, respectively. W is the most erosion resistant, relatively, among these materials. The relatively low erosion rate of W is due to its higher value of the heat of sublimation and a high threshold for sputtering which is above 100 ev when monoenergetic hydrogen species are the impinging ions. However, with a 50% mixture of deuterium and tritium and a Maxwellian distribution of ion energy the sputtering threshold for W is reduced to about 10 ev [6]. With the measured gross peak erosion rate of W at 0.1 nm s 1 from DiMES, when extrapolated to an ion flux of m 2 s 1, the corresponding gross erosion rate is about 0.3 nm s 1, which would represent a full power lifetime of 77 days for a2mmthick W coating. This lifetime can possibly be increased by a factor of ten to about 2 years when the redeposition effect is included [7]. In order to increase the W-coated divertor lifetime to the design goal of 3 full-power-years, the ion temperature at the divertor will have to be reduced to approaching the physical sputtering threshold of 10 ev. Based on the above observations, the edge ion temperature resulting from the radiative approach of the ARIES-RS divertor design presented in the last section is in the range of 8 35 ev. Therefore, there is a good possibility that the reference 2 mm thick W coating will satisfy the divertor lifetime goal of 3 full-power-years. This will have to be demonstrated by future experiments. In addition to the need for fundamental net erosion data of W from sputtering yield experiments and from D-T burn Tokamak experiments, there are other issues that will impact on divertor components lifetime and will have to be addressed. Some of these issues are: With the V-alloy first wall ARIES-RS design, impact on the W erosion rate from the additional sputtering of the V-alloy background and from W self-sputtering will have to be considered. The surface chemical reactivity of W-metal with plasma contaminants such as oxygen, which can have significant impact on the erosion rate, must also be considered. In addition to surface erosion there are also the concerns of high-z core contamination from the migration of W-ions from the divertor under normal operation, and the spread of W particulates to the first wall during startup and under disruptive events. However, recent favorable results from ASDEX-Upgrade show that the migration of W from its divertor is acceptable [8]. Impacts from ELMs and surface arcing of W will have to be evaluated. The latter is suggested by the observed, yet unexplained, phe-

6 120 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) nomenon indicated by the DiMES DIII-D results [5]. 6. Divertor module design 6.1. O erall description The ARIES-RS divertor system has a doublenull configuration with symmetry about the reactor midplane. There are 16 blanket/shield sectors, each with a pair of top and bottom divertor modules. Each module consists of three plates: the inboard (IB) plate, the dome (D) plate and the outboard (OB) plate. Fig. 1 shows the divertors as they are located in the reactor sector and Fig. 2 shows a cross-sectional view of the sector. Fig. 3 shows the separations between the IB, D and OB plates. The between-plate slots are there to allow pumping of the neutrals: D 2, T 2, He and Ne impurity used in the radiative divertor scheme. The neutrals accumulating at the throats of the divertor slots enter the pumping plena and are pumped out by the reactor vacuum system. Fig. 4 is a schematic of the divertor plate showing the internal geometry. There are three zones: the front zone consists of 2 mm thick W tiles and is the surface which faces the plasma and experiences ion impingement; the second zone is an 8 mm thick V-alloy structure that contains the coolant channels which have rectangular crosssections with nominal dimensions of 4 8 mm. Fig. 4. ARIES-RS divertor plate and coolant channels. The last zone is also constructed from V-alloy and is 40 mm thick. This zone acts as the structural component for the plates lending them rigidity and stability. Coolant manifolds are located toroidally at the ends of each plate at the back, out of reach and sight of the plasma. Fig. 5 shows the coolant routing of all three divertor plates. The supply and return manifolds are indicated as are the coolant flow directions. The inboard divertor slot is located between the supply manifold of the inboard plate and the supply manifold of the dome plate. Similarly, the outboard divertor slot is situated between the return manifold of the dome plate and the supply manifold of the outboard plate. It is interesting to note that in all three cases, the toroidal width of the plates increases in the same direction as the coolant flow. To maintain a constant flow velocity in the channels while still providing the coolant Fig. 3. ARIES-RS divertor geometry. Fig. 5. Divertor plates and coolant manifolds.

7 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Table 2 Divertor plates geometric parameters Inboard Dome Outboard Front surface area (m 2 ) Top to bottom distance (m) Short toroidal dimension (m) Long toroidal dimension (m) Number of coolant channels in plate Mass of plate (kg) Average increase in toroidal dimension from 300 to 873 K due to thermal expansion (cm) coverage on the plates, the aspect ratio of the channels will be changed, holding the cross-sectional area constant. Table 2 gives the geometric parameters of the divertor plates. The divertor plates will be supported on the structural ring which surrounds the reactor core and constitutes part of the blanket reflector. These supports will be made adjustable such that the plates can be properly aligned during installation Fabrication of the di ertor modules The divertor plates are fabricated from the V-alloy V 4Cr 4Ti and have 2 mm thick surface castellated W coating bonded to the surface facing the plasma. Two methods have been proposed for fabricating the plates, both of which depend on the ability to perform diffusion bonding of V-alloys. Although there is no reason to doubt that V-alloys can be diffusion bonded, there has been no experience to date in this area. Vanadium is a refractory metal possessing high temperature capability, and for this reason diffusion bonding would require higher temperatures than is commonly applied for diffusion bonding of steel alloys and other common metals. Fig. 6 shows the first proposed method for fabricating the divertor plates. A 6 mm thick V-alloy plate is cut and bent to the required shape. The shaping is compounded by the fact that all the plates have both toroidal and poloidal curvature. A computer controlled mill is then used to machine the 4 mm deep channels. This technology is in hand and can be easily implemented. Next, a 1 mm thick sheet is cut to size and shape, and then diffusion bonded to provide the closure for the channels. Now comes the most difficult part of the process, and that is the attachment of the 40 mm thick backing plate. Cutting, bending and fitting up such a plate in preparation for diffusion bonding to the coolant assembly will be quite challenging. The next step is to weld on the manifolds. Finally, the last step in the fabrication is to apply the W castellations. Here again, there is no experience in attaching W to V-alloys. Brazing might be an option using high temperature brazing materials. One such example is V 30Nb 5Ta which melts at 1815 C but has a remelt temperature of 2300 C. Fig. 7(a) and (b) are perspective views of the assembly steps for the outboard plate showing the compound curvatures that are required. An alternate method for fabricating the plates is shown in Fig. 8, requiring only one diffusion bonding step. In this method a cast or forged plate block is used which has already been radiographed for imperfections. The block is machined Fig. 6. Steps in fabricating divertor plates.

8 122 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Fig. 9. ARIES-RS divertor/fw configuration Support and alignment of di ertor plates Fig. 7. (a) Steps in assembling a divertor plate; (b) steps in assembling a divertor plate (continued). to the required size and shape, after which the channels are machined into it. The closure for the channels is then diffusion bonded to the block. The remaining steps will be the same as in the previous assembly procedure. Fig. 8. An alternate method for fabricating divertor plates. The divertor plates are supported on the structural ring which subtends the reactor plasma core and makes up part of the reflector. This structural ring shown in Fig. 9 is the common element which holds together the inboard and outboard replaceable blanket/shield components. Fig. 9 shows the divertor plates supported on bolts fixed to the structural ring. One of these bolts is shown in Fig. 10. It is made of V-alloy, hollow and threaded with opposing threads on either end. Each bolt will have a hexagonal hole on the end which attaches to the structural ring. The plates are aligned by turning the bolts with a hex wrench from the outside of the structural ring. The number, location and orientation of the bolts depends on the total force on the plate from the worst vertical displacement event (VDE), and on the requirements for alignment. The mass of the plates at kg (Table 2) is small compared to the disruption loads and thus, the disposition of the bolts will depend on the magnitude and direction of the disruption forces. Table 3 gives the peak disruption forces on the center and outboard divertor plates. For this evaluation we will focus on the outboard plate because it is the largest of the three divertor plates and has the highest peak loads. The table gives the peak force due to a 10 ms plasma quench with no plasma movement and a 2500 ms plasma drift with a 10 ms quench. The latter case gives the highest peak loads which for the outboard plate

9 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) MPa. To determine the type of loading on the plate we have to calculate the natural frequency, which for a rectangular plate simply supported along all edges is given by [9]: f= K n Dg in Hz 4 2 a where D is the plate flexural rigidity, g is the gravitational acceleration, is the loading pressure including the mass of the plate, a the plate short dimension and the constant K n is given as [10]: 2m bn 2 K n = 2 m 2 a + a b Fig. 10. Connection of divertor plate and structural ring. are 0.98 MN in the radial direction and 1.8 MN in the vertical direction. A negative sign means the force is inward, or towards the plasma. Since the plate is predominantly vertical, we will first address the horizontal force which tends to push the plate towards the axis of the Tokamak, putting the bolts in tension. This pressure per outboard plate is 0.98 MN/16(2.03 m 2 )=0.032 where m a and m b are vibration modes in the a and b directions (b is the plate long dimension). The flexural rigidity of the plate D= t 3 /12(1 2 ) for V 4Cr 4Ti at 600 C is 1.2 MNm where is the Young s modulus, is the Poisson s ratio, and t is the plate thickness. Using m a =m b =1 for a/b= 0.6 gives K n =13.4 and a = MP we obtain f=54 Hz. This frequency has a natural period of 18.5 ms. The rise time constant for the load is 2 3 ms. Assuming a triangular load pulse with a t d /T=4/18.5 to 6/18.5=0.22 to 0.32 where t d is the load pulse and T is the natural period of the plate. The dynamic load factor (DLF) for such a system is between 0.6 and 1.0 [10] of the static load condition. To be on the conservative side we use a DLF of 1.0. The bolt shown in Fig. 10 has an outside diameter of 2.5 cm and an inside diameter of 2.0 cm with a cross-sectional area of 1.77 cm 2. The resultant force vector composed of the vertical force (1.8 MN) and the horizontal force (0.98 Table 3 Peak disruption forces on divertor plates Case Maximum stress (MPa) Peak r force (MN) Peak z force (MN) Center divertor plate 10 ms quench ms plasma drift with a 10 ms quench Outboard divertor plate ms quench ms plasma drift with a 10 ms quench

10 124 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Fig. 11. Divertor plate support bolts attachment. MN) is 2.05 MN or MN per module for the outboard plate and is oriented at an angle of 29 to the vertical. For a DLF of 1.0 the loading we use is the static load of MN which requires 7.3 bolts at a stress of 100 MPa. Eight bolts spaced at 62 cm along the long dimension and 56.5 cm along the short dimension, oriented at 29 to the vertical will be required to support the outboard plate module against the worst vertical disruption event. The estimated nuclear heating in the bolts will be dissipated by radiation to the cooled support ring. The central plate has a surface area smaller than the outboard plate and the peak forces as shown in Table 3 are smaller by a factor of 2 3. Supporting it would be simpler than the outboard plate. The bolts are also used to align the plates within the blanket/shield sector. Fig. 11 shows how a bolt is attached to the structural ring while passing through coolant channels. This is performed at the factory during the assembly of the sector. When the fusion power core sector is inserted into the vacuum chamber torus, proper alignment of the whole sector is performed using the sector hydraulic alignment mechanism Summary of di ertor module design The divertor modules design can be summarized by the following: The divertor plates are made of the V-alloy V 4Cr 4Ti. They are 4.8 cm thick including 2 mm W castellations on the surface facing the plasma. They have rectangular coolant channels running in the direction of the short dimension of the plate. Fabrication of the plates depends on the ability to diffusion bond large complex V-alloy to V-alloy plates and on the ability of applying W castellations on the surfaces facing the plasma. Support of the plates is dominated by the electromagnetic forces due to VDE. The outboard plate will require eight supporting bolts spaced at 60 cm and oriented at 29 to the vertical to react the dynamic loading from a VDE. The plates are aligned within the reactor sectors by turning the support bolts. Subsequent alignment of the sectors in the reactor torus is performed with the hydraulic sector alignment system. 7. Power distribution and heat transfer design Power and heat flux distribution of the ARIES- RS divertor are estimated from the physics analysis followed by 3-D radiation calculations. Heat transfer calculations of the outboard divertor with handling of more than 40% of the total power are performed to determine the temperature distributions of the selected design. Results of these calculations are then used for structural analysis presented in Section Power and heat flux distributions The functional goal of the ARIES-RS divertor is to limit the maximum heat flux to the divertor target plate to 5 MW m 2. To achieve this limit, we propose to use the radiated divertor operating mode as presented in Section 4. The divertor heat flux distribution consists of contributions from particle impingement, radiation from the plasma core and radiation from the four regions of strong Ne impurity radiation. A particle impingement heat flux of 4 MW m 2 was estimated by physics calculation. A uniform radiation from the plasma core is obtained from results of the ARIES-RS system study. The magnitude, location, and geometry of the four neon radiation regions at each

11 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Table 4 Global divertor-power balance System results Alpha power, P (MW) Bremsstrahlung power, P brem (MW) 56.4 Line radiation, P line (MW) 25.4 Current drive power, P cd (MW) 80.8 Total-P transport =(P P brem P line +P cd ) (MW) Radiation Scrape-off layer radiative power, P sol rad 8.0 (MW) Outboard-ring power (MW) Inboard-ring power (MW) 76.2 Uniform radiation power* (MW) 81.8 Particles power (MW) 82.2 Total * Uniform radiation from the remaining divertor volume=70 (Pout)+11.8 (Pin, adjusted) (MW). Fig. 12. Outboard divertor plate heat flux distribution. of the divertor slots are also provided from the physics analysis as shown in Fig. 9 and Table 4. The sum of these heat flux contributions forms the input for detailed heat transfer evaluation. The global power balance is given in Table 4. A 3-D toroidal geometry radiation model [11] is used to calculate the heat flux distribution in the plasma chamber by accounting for all of the radiations from the plasma core and around the divertors. Since the heat flux distribution on a receiving surface is very sensitive to its relative geometric orientation and configuration to the given radiation sources, this 3-D model is used as a design tool to perform the design iteration between the geometry and orientation of the outboard divertor plate and its heat flux distribution. The resulting thermal power distribution in the plasma chamber is given in Table 5. As shown, the outboard divertor plates are receiving MW, 40% of the total divertor power. Fig. 12 shows the total heat flux as the sum of particle heat flux and radiation heat flux. It shows the two maximum heat flux peaks of 5.71 MW m 2 (at the strike point) and 5.8 MW m 2 (30 cm away Table 5 Distributed thermal power in the plasma chamber Component Power (MW) Area (m 2 ) Average heat flux (MW m 2 ) Outboard first wall Inboard first wall Outboard plate Divertor dome Inboard plate Total Transport power: P +P cd = =513.2 MW.

12 126 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) from the strike point, and closest to the outboard radiating region). The rest of the radiation distributed to the inboard divertor and first wall is also calculated and used as inputs to the divertor and first wall heat transfer calculations, respectively. The heat flux distribution of the first wall is given in Table 6. The first wall heat flux consists of mostly bremsstrahlung radiation from the core and additional radiation from all the divertor sources. Similarly the divertor heat flux consists mostly of radiation from the divertor sources and an additional contribution from the core Coolant routing and heat transfer design The divertor module illustrated in Fig. 3 consists of the target plates and structure. The target plates are represented by the inboard, outboard and dome surfaces. They are mechanically connected to the Tokamak structural ring through strong adjustable screw-type attachments (described in Section 6.3). The vacuum pumping plena are located behind the dome. Detailed divertor surface configuration is defined by the following criteria: Outboard divertor plates intersect the magnetic field line at 15, and the inboard divertor plates intersect the magnetic field line at 56. These are selected from the tailoring of maximum surface heat flux to 6 MW m 2 and to minimize the particle flux going back to the plasma core through geometric baffling. (The original design goal of 5 MW m 2 is not met but the design still satisfies all material design limits.) Fig. 2 shows the cross-section of the reactor sector including the FW/blanket and Table 6 First wall heat flux distribution (MW m 2 ) a Z-location (m) Inboard (Midplane) a Bremsstrahlung+divertors radiation. Outboard Fig. 13. Divertor plates and structure coolant routing. structural ring. The entire coolant is routed through the outboard divertor plates and then the dome and inboard plates, before cooling the structure at the back. The distribution piping and plena are all fitted behind the divertor surfaces as shown in Fig Principal considerations With outboard divertor heat flux distribution given in Fig. 12, the outboard divertor plates have to be designed to handle a maximum heat flux of 5.8 MW m 2 and an average value of 1.92 MW m 2. An additional requirement is to have a high outlet coolant temperature suitable for a high efficiency power conversion system. The latter is necessary because the thermal power received at the divertor region (surface heat flux +nuclear heating) amounts to about 15% of the total fusion power core thermal power. About 70% of the divertor thermal power is in the form of surface heat flux and 30% is volumetric heating. The coolant routing scheme is selected to maximize coolant exit temperature from the outboard plate to about 460 C, allowing an efficient removal of surface heat flux while meeting the first design limitation of maximum structural material temperature. The second design limitation is the thermal stress. In the first approximation, the thermal stress of a plate is proportional to the difference between front surface temperature and the mean temperature of the plate, while assuming plane strain boundary conditions. The maximum surface temperature can be minimized by making the coolant channel wall as thin as possible. To further reduce the temperature difference, a higher

13 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) mean temperature for the structure can be achieved by increasing the thickness of the structure at the back by a few centimeters. This approach of a thicker plate would also improve the shielding effectiveness of the divertor structure and be more effective in withstanding mechanical loads caused by plasma disruptions. In terms of temperatures and stresses there are three critical locations at the outboard divertor plates. One of them is the strike point, the location of one of the two peak heat fluxes. The inlet coolant is arranged to be directed as close as possible to this strike point in order to minimize the local temperature. The second critical location is 30 cm away from the strike point where the second peak heat flux was identified. The third critical location is the coolant exit where the coolant temperature is at 610 C Coolant routing The selected lithium coolant routing is shown in Fig. 13. There is one inlet tube and one outlet tube for each divertor region. The inlet and outlet coolant manifolds are welded to the plates and connected to the divertor structure. The entire coolant with an inlet temperature of 330 C is routed through the outboard divertor plates, it then cools the other two plates and structure in order to remove the power at MW (65.5% of total surface heating) and handles the peak heat flux of 5.8 MW m 2 at 30 cm away from the strike point while maintaining the maximum V-alloy temperature to lower than the design limit of 700 C. In the divertor structure, the coolant continues to heat up to the desired outlet temperature of 610 C. Here the temperature difference between the structure and the coolant can be maintained at a rather low value due to the relatively low volumetric heating rate in this zone Heat transfer design for the di ertor plates The heat transfer design of the lithium-cooled outboard plates is evaluated. It removes 65.5% of surface heating or 49.7% of the total divertor thermal power. The lithium coolant inlet/outlet temperatures of 330/610 C are selected to achieve the same coolant conditions as the lithium-cooled blanket. Successful development of the MHD insulator between the coolant and the V-alloy coolant channel is assumed. No penalty on pressure drop is assumed to be caused by the MHD effect. The total divertor coolant flow rate is given by the balance of thermal power. Rectangular coolant channels have been selected because they offer the shortest distance between the highly loaded front surface and the bulk of the coolant flow. Fig. 8 shows a cross-section through the plate with the coolant channels having dimensions of 4 8 mm. This results in a lithium velocity of 4.74 m s 1. Including turns, contractions and expansions the estimated total pressure drop of the divertor fluid flow is 0.45 MPa. Fig. 12 shows the surface heat flux profile along the outboard divertor target. The lithium-cooled divertor plate was analyzed using the ANSYS code [12] to establish the temperature profiles resulting from the applied surface heat flux profile with an average of 1.92 MW m 2 and a peak of 5.8 MW m 2. The 3-D heat transfer was modeled as a 2-D transient calculation. This is a possible approach in the MHD laminar flow situation by a simple transformation of the energy equation. The axial flow direction is replaced by a time coordinate. The velocity profile in coolant channels is assumed to be slug flow and fully-developed throughout the entire channel. It should be noted that based on this 2-D representation, the variations in the coolant channel crosssection resulting from the changing major radius of the toroidal geometry are assumed to be negligible. Thermal hydraulic parameters for one of the outboard divertor target plates are summarized in Table 7. Table 8 gives a summary of thermal hydraulic design results for the outboard divertor target plate. The axial temperature profiles are plotted in Fig. 14 at various locations throughout the coolant channel cross-section. The represented locations are at W surface, W V interface, V Li interface at front, front region of the Li coolant, centre of the Li coolant, back region of the Li coolant, V Li interface at the back and V-surface at the back plate. As shown, the maximum V-alloy temperature is less than the design limit of 700 C and the maximum W coating temperature

14 128 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) is 771 C which should be acceptable as a nonload-bearing element of the divertor design. 8. Coolant channel structural analysis 8.1. Introduction and summary Structural analysis of the ARIES-RS divertor concept is completed using 2-D and 3-D finite element structural models input to the COSMOS and ANSYS codes [12,13]. The 2-D models are used primarily to provide design guidelines for deducing the maximum thermal stress intensities. The design recommendations resulting from the 2-D models include cutting vertical slits through the tungsten and vanadium between coolant channels and castellating the 2 mm tungsten layer in the poloidal and toroidal directions of the divertor. Also, it has been determined that the divertor should be supported in such a way to allow for thermal growth and rotation of the cross-sections while maintaining capability to react to disruption halo current loads. These requirements are input as boundary conditions to a 3-D model of a single coolant channel of the outboard divertor. A steady-state heat transfer analysis is performed to calculate the thermal gradients which are input to the 3-D structural model which included the ef- Table 7 Thermal hydraulic parameters for 1/32 divertor module Coolant Li Structural material V 4Cr 4Ti Armor W Thermal power from divertor plate surfaces (MW) Thermal power from nuclear heating 4.75 (MW) Total thermal power of divertor (MW) Total area of 1/32 divertor surface (m 2 ) 5.67 Average surface heat flux (MW m 2 ) 1.92 Coolant inlet/outlet temperature ( C) 330/610 Total coolant volumetric flow rate (m 3 s 1 ) Coolant velocity in inlet/outlet tubes 1.0 (m s 1 ) Coolant velocity in manifolds (m s 1 ) 0.5 Table 8 Summary of thermal hydraulic design results for 1/32 outboard divertor plate Outboard plate surface area (m 2 ) 2.10 Average surface heat flux (MW m 2 ) 3.39 Thermal power from heat flux (MW) 7.12 Thermal power from nuclear heating (MW) 0.65 Total thermal power of outboard divertor plate 7.77 (MW) Coolant channel dimension (mm) Divertor plate total thickness (cm) 5.0 Length of outboard divertor plate (m) 1.12 Total number of coolant channels 190 Average coolant velocity (m s 1 ) 4.74 Temperature at three critical locations 1 At the strike point Surface heat flux (MW m 2 ) 5.71 Maximum temperature in V-alloy tube wall 527 ( C) Maximum temperature in W armor ( C) 625 Maximum temperature in V-alloy local 516 shield ( C) 2 Thirty centimeters from strike point Surface heat flux (MW m 2 ) 5.80 Maximum temperature in V-alloy tube wall 681 ( C) Maximum temperature in W armor ( C) 771 Maximum temperature in V-alloy local 538 shield ( C) 3 At the coolant exit Surface heat flux (MW m 2 ) 0.62 Maximum temperature in V-alloy tube wall 517 ( C) Maximum temperature in W armor ( C) 528 Maximum temperature in V-alloy local 632 shield ( C) fects of a castellated and uncastellated tungsten layer. For both cases the maximum stress intensities exceeded the elastic stress allowable for the vanadium of 330 MPa. However, the results for the castellated tungsten case indicate that the design should be able to satisfy the inelastic criteria specified in code case N of the ASME Code [14]. Other outstanding structural concerns about the divertor design are: (1) the residual stresses developed during the process of bonding tungsten to vanadium; (2) stress singularities at free edges of the tungsten/vanadium interface which may result in debonding failures; and (3) detailed design and testing of the co-axial bolted

15 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Fig. 14. Temperature distributions at different locations of the outboard divertor plate. divertor support to allow unrestrained thermal expansion of the divertor and adequate transmission of halo current loads to the vessel Structural models The ARIES-RS divertor consists of a large vanadium alloy V 4Cr 4Ti plate 48 mm thick bonded to 2 mm of tungsten for surface erosion resistance. The plate is cooled by liquid lithium flowing in 4 8 mm rectangular channels located 1 mm beneath the tungsten and V-alloy interface. The outboard coolant channels are 1.2 m long and each divertor sector is about 2 m wide. The surface heat flux varies poloidally as shown in Fig. 12 and results in the temperature distributions shown in Fig. 14. Details are presented in Section It can be seen that an accurate stress analysis of the divertor plate requires a 3-D structural model. However, for estimating the stresses due to the thermal gradient through the plate thickness a 2-D stress analysis is useful for design evaluation. In addition, the effects of castellating the tungsten layer and inserting slits between the coolant channels can be investigated using a 2-D model. The first 2-D model shown in Fig. 15 assumes generalized plane strain conditions in the poloidal and toroidal directions of the divertor plate. Generalized plane strain conditions require constant thermal growth of the cross-sections (i.e. no rotation of the cross-section is allowed). These displacement conditions are achieved by using eight node solid elements modeled for input to the COSMOS code and utilizes coupling constraints on the nodes of the appropriate planes. These plane strain conditions result in a structural model that is conservative for temperature loads since rotation of the cross-sections in two planes is prevented. Nevertheless, there is little recourse in developing a 2-D model to accurately represent a large structure, especially since the method of attaching the divertor to the vessel has not been designed during this initial phase of evaluation. Results from the first 2-D model showed that cutting vertical slits through the tungsten and vanadium between coolant channels produce significant stress reduction. The slits are modeled by simply removing the coupling constraints along the sides of the coolant channel. The 2-D generalized plane strain model proved to be too conservative. The non-rotational constraints imposed on the cross-section produced

16 130 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Fig. 15. Generalized plane strain model of the divertor. calculated stress intensities that exceeded the 3Sm limit (330 MPa) for the vanadium [15]. As a design stress limit, it would be desirable to limit the thermal stress to 200 MPa to allow 130 MPa for mechanically induced stresses. It should be noted that no stress limits are imposed on the tungsten as it is permitted to crack providing it remains bonded to the vanadium. The preliminary results showed the need to design a support for the divertor that will allow nearly free thermal growth but still be capable of reacting halo current loads. Assuming this to be possible, the coupling restraints were removed from all faces of the 2-D model to allow the cross-sections to rotate. The nodal temperature for the 2-D models are input by hand based on the peak temperatures at time=0.15 s (Fig. 14), corresponding to the outboard strike point location, calculated by the heat transfer analysis presented in Section Table 9 presents the temperature dependent material properties used as input to the structural models based on information from [15]. A more accurate structural model of the divertor was developed using a 3-D representation of a single coolant channel and the back structure (Figs. 16 and 17). A total of solid elements are required to adequately model the full length of a single coolant channel. The boundary conditions assumed for this model allow the free thermal expansion poloidally from fixed points at the bottom, center of the coolant channel. Also, the cross-sections in the toroidal direction are allowed to rotate. The temperature distribution throughout the model was calculated using the steady state surface heat flux shown in Fig. 12 and a constant film coefficient for liquid lithium flow. The calculated temperature distribution for the 3-D model is shown in Fig. 18 and agrees reasonably well with the results presented in Section Analytical results The best results for the thermal stress intensity from the 2-D model with plane strain conditions in the poloidal and toroidal directions are shown in Fig. 19. The model includes the effects of Table 9 Thermal hydraulic parameters for 1/32 divertor module Material Temperature ( C) E (10 5 MPa) (10 6 C 1 ) V 4Cr 4Ti Tungsten

17 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Fig. 16. The 3-D thermal stress model for the single coolant channel of divertor. vertical slits through the tungsten and vanadium to the bottom of the coolant channel. Plane stress conditions are specified for the tungsten and an element is deleted to gain maximum benefit from castellation. The maximum stress intensity in the vanadium calculated for this conservative model is 424 MPa and is due primarily to the tensile stress in the poloidal direction developed in the coldest section of the vanadium. Although the maximum stress intensity for this model exceeds Fig. 17. The 3-D thermal stress model of the single coolant channel. the elastic stress criteria (3Sm =330 MPa) for the vanadium material at 350 C, the stresses can be reduced by allowing the cross-section to rotate. The maximum stress at the boundary of the coolant channel due to thermal loads only is 192 MPa. Examination of the plot presented in Fig. 19 shows the deformed shape of the thin vertical legs of the coolant channel and the benefit that the slits provide in reducing the maximum stress intensities. The 2-D model was modified to allow rotation of the cross-sections in both the poloidal and toroidal directions of the divertor. These boundary conditions assume that the divertor can be supported in a manner to allow free thermal expansion of the divertor and still transmit disruption halo current loads to the vessel. A possible solution to this problem is presented in Section 6.3. The results of this modification are shown in Fig. 20 for the case in which the tungsten layer is assumed to have been castellated at a stiffness of nearly zero. The maximum stress intensity in the vanadium for this case is 219 MPa and satisfies the stress criteria (less than 3Sm= 330 MPa). The nodal temperature distribution for the 3-D model (Fig. 18) is input to the structural model for the ANSYS code to perform the thermal stress analysis. The boundary conditions input to the model shown in Fig. 17 assume that each segment is fixed at the center, bottom of each coolant channel. The divertor is also assumed to be free to expand toroidally and accounts for the restraint resulting from the thermal gradient in the poloidal direction as well as through the thickness. A deformed plot of the divertor due to thermal loading is shown in Fig. 21. The maximum resultant displacement is 0.48 cm. The thermal stress intensities in the divertor are calculated for two cases: 1. The tungsten layer is not castellated or castellated in the poloidal direction. 2. The tungsten layer is castellated and has a stiffness of nearly zero (Young s modulus=10 MPa). The stress intensity results for the vanadium for Case 1 are shown in Figs. 22 and 23. It can be seen

18 132 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Fig. 18. Temperature distribution in divertor for steady-state heat flux. Fig. 19. Vanadium stress intensity plot for uncastellated tungsten. Fig. 20. Vanadium stress intensity plot for castellated tungsten.

19 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Fig. 21. Deformed plot of divertor due to thermal loads. that the maximum stress intensity of 593 MPa occurs near the location of the maximum temperature and at the free edge with the tungsten interface. This is at a location of a stress singularity and therefore is not a correct value. The finite element method cannot be used to evaluate the state of stress at the free edge interface between different materials because the shear stresses do not satisfy equilibrium at these locations. However, stress singularities are indeed locations of high shear stresses that can produce a debonding failure between the tungsten and vanadium. The only way to determine whether or not a debonding failure will occur is by cyclic testing of the component under the applied thermal loading. Also, the residual stresses due to the process used to bond the different materials can have an effect on the fatigue life of the component. The stress distribution in a segment of the divertor shown in Fig. 23 is seen to be different from that computed by the 2-D model. The maximum stress intensity calculated by the 2-D model occurs below the coolant channel. The maximum stresses calculated by the 3-D model occur at the interface between the tungsten and the vanadium. Examination of the stress components indicate that the compressive stress in the poloidal direction is the primary contributor to the calculated stress intensity and is due to the poloidal thermal gradient and the differential thermal expansion between the tungsten and vanadium. This effect, of course, cannot be accounted for with the 2-D model. The stress intensity results of Case 2 (castellated tungsten) are shown in Figs. 24 and 25. The stress distribution is similar to that for Case 1, but the maximum value is reduced to 369 MPa and is not influenced by stress singularity effects. This value still exceeds the stress criteria for elastic stress analysis, but indicates that the creep-fatigue criteria for inelastic analysis can most likely be satisfied. The stress criteria for inelastic analysis is specified in code case N of the ASME boiler and pressure vessel code [14]. This code case provides an alternate criteria when the criteria for elastically calculated primary plus secondary stresses exceed the 3Sm limit. The combined effects of creep-fatigue damage are evaluated by elastic-plastic-creep analyses and limit the accumulated damage to specified values. Since vanadium is not an ASME code material, the creep-fatigue damage limits for stainless steel would be recommended. Creep rupture data for vanadium and fatigue data based on strain range would be required for implementation of code case N Particle exhaust and vacuum system design The design of ARIES-RS [16] generates a few important boundary conditions for the pumping system design. First, the fusion reaction rate is given as 2167 MW, which implies a helium production rate, F, at s 1. In steady state, when calculating the pumping requirement, the exhaust rate of helium must equal the production rate. The core plasma helium fraction, obtained from the transport analysis, is One further assumption needed to complete this analysis is the pumping plenum enrichment factor,, for helium, i.e. f plen /f core where f plen(core) is the ratio of the helium ion density to the total electron density of the plenum (core). Based on data from JET, ASDEX Upgrade, and DIII-D, is conservatively assumed to be 0.2. The pumping speed of the exhaust pumps, L pump in m 3 s 1, is assumed to be equal for deuterons, tritons, and helium, and can be adjusted to give a reasonable total plenum pressure (based on existing data, several millitorr is reasonable). In steady state the exhaust rate of helium must equal the source implying that the helium density in the plenum is given by, N HePlen =F/L pump.

20 134 C.P.C. Wong et al. / Fusion Engineering and Design 38 (1997) Fig