AN ADVANCED COMPUTATIONAL APPROACH TO SYSTEM MODELING OF TOKAMAK POWER PLANTS

Transcription

1 AN ADVANCED COMPUTATIONAL APPROACH TO SYSTEM MODELING OF TOKAMAK POWER PLANTS Zoran Dragojlovic 1, Charles Kessel 2, Rene Raffray 1, Farrokh Najmabadi 1, Lester Waganer 3, Laila El-Guebaly 4, Leslie Bromberg 5 1 University of California in San Diego, La Jolla, CA, zoran@fusion.ucsd.edu 2 Princeton Plasma Physics Laboratory, Princeton, NJ, ckessel@pppl.gov 3 St. Louis, MO, lesw@centurytel.net 4 Fusion Technology Institute, University of Wisconsin, Madison, WI, elguebaly@engr.wisc.edu 5 Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge MA, brom@psfc.mit.edu A new computational model for fusion power plant system studies is being developed for the ARIES program. An operational design space has been created to explore the most influential parameters in the physical, technological and economic trade space related to the developmental transition from experimental facilities to viable commercial power plants. This allows examination of a multi-dimensional trade space as opposed to traditional sensitivity analyses about a baseline design point. The influence of multifunctional, highly dependent parameters can easily be visualized, which may highlight one or a few difficult-to-achieve parameters that would yield a highly acceptable design solution. The new ARIES systems code consists of adaptable physics, engineering and costing modules which capture the current tokamak knowledge database and reflect both near-term as well as advanced technology solutions that are higher risk but have higher performance potential. To fully assess the impact of the range of physics and engineering implementations, the plant cost accounts have been revised to reflect a more functional cost structure. All of these features have been validated against the highly respected ARIES-AT baseline. The present results demonstrate novel visualization techniques for trade space assessment of attractive tokamaks for commercial use. I. INTRODUCTION Conceptual power plant systems analysis codes can be traced back to TOCOMO (TOkamak COst MOdel) 1, which was adapted for STARFIRE in the 1980s and provided a basis for GENEROMAK code 2. The latter laid a foundation to ARIES design concepts of the 1990s, such as ARIES-II, IV, SPPS and AT 3. The ARIES systems algorithm used for these designs had a physics basis that is comparable to MUMAK code 4 and was benchmarked with TRAC-II 5, SUPERCOIL and SCAN codes 6. The aforementioned algorithms had a systems analysis approach which consisted of designing the optimal reactor and exploring the sensitivity of this design to local perturbations in the most critical parameters. However, the search for a single optimal point is not sufficient to identify a vast space of possibly attractive near optimal designs and often has a difficulty to justify the selection of that particular point. As a better alternative, a parametric design space approach is utilized with a goal to highlight the tradeoffs over wide intervals of physics and engineering parameters that may lead to the lowest cost of electricity. Recent work by Hiwatari et al. 7 demonstrated a similar approach as a way to lay out a development path for early realization of fusion-driven electric power, immediately following the ITER. The ARIES program, however, is focused on identifying the research and development needs in transition from experimental tokamak facilities to fully operational "tenth-of-a-kind" power plants which use a mature fusion technology of the future. In order to fulfill this objective, a new systems code is being developed as a computational tool that integrates the state-of-art physics, engineering, design and costing algorithms. The structure of the systems code is modular and composed from a custom-made toolbox of generic, easy-to-assemble building blocks. The steady state plasma physics for advanced tokamaks is modeled by an algorithm that was originally developed in order to examine the high field compact tokamak burning plasmas for the design study Fusion Ignition Research Experiment (FIRE) 8. The power core and energy conversion systems are modeled based on the ARIES-AT design 9. The magnetic confinement model resembles the one used for the ARIES-AT in geometry, while the material composition is modified in order to utilize a less advanced technology and a more realistic costing. The structural support of the toroidal field (TF) magnet is estimated by scaling from the finite element analysis reported in 10. The breakdown of all the power plant costs has been updated through the FUSION SCIENCE AND TECHNOLOGY VOL. 56 AUG

2 recent ARIES design concepts, such as II, IV, SPPS, and AT 3. Coding style and building blocks of the new systems algorithm are described in Section II. Validation of the algorithm and visualization of data are discussed in Section III. II. ARIES SYSTEMS CODE ARIES systems code consists of three distinctive modules, which are physics, engineering and costing, as shown in Fig. 1. The physics module generates a large database of viable plasmas for advanced, high energy tokamaks. Engineering module creates a power extraction and conversion system, including the 3-D power core and the power flow model from nuclear fusion to net electric power. Costing module estimates the cost of the power core and all the costs associated with the plant development, operation and maintenance. Cost of electricity is the final output of the systems code. Fig 1. ARIES systems algorithm flow chart. The foundation of the algorithm is a general purpose systems analysis toolbox. This toolbox consists of readyto-use generic C++ classes, which serve as building blocks for the power plant model. Class DesignPoint holds design specific data and functions that describe the entire machine, including plasma parameters, power core builds, power flow, etc. Class Part holds part-specific information, such as geometry, composition, material properties and costs. Class CostingAccount contains the costing account structure for a given machine. A model of the power plant is generated by building the power core from pre-defined parts, setting all the desired machine properties and functions within the DesignPoint object, defining the CostingAccount structure and connecting all these elements together in order to estimate the cost of electricity. The custom-made toolbox of C++ classes described here was built for a wide scope of possible applications in systems analysis of power plants. Object-oriented programming was used in order to allow for division of a complex algorithm into independent data structures (objects) which can be handled independently from each other, thus allowing for efficient software development. The algorithms presented in this paper were written for tokamaks that are similar in configuration to the ARIES- AT but allow for a variety of different options, such as plasma shape and size, blanket configuration, and type and size of the magnets. Major assumptions and limitations of the present model are listed as follows: Power Core: Global plasma power and particle balance equations are solved by 0-D analysis, assuming coronal equilibrium. Density and temperature profiles were chosen to provide a reasonable match to those obtained by 1.5-D analysis 8. The aspect ratios of different plasma are limited to those greater than 3. The current drive is supported by bootstrap currents. The toroidal and poloidal field magnets are superconductors. No modular maintenance is considered, only full sector, horizontal maintenance. No redundant components of the power core are included, except for the lower PF coils. Blanket concepts are limited to LiPb/SiC and DCLL, at present. All major power core components are life-of-plant except for replaceable components. Power Flow: Only DT fuel cycle is considered in this study. Thermal power conversion occurs through either Brayton or Rankine cycle, depending on the blanket option. No direct conversion of radiation into electricity is considered. The work supplied to heat transfer fluids is recovered as useful heat. Power Plant Model: "Tenth of a kind" commercial power plant is assumed, which affects maintenance, reliability, inspectability, availability and costing. No development costs are included. II.A. Power Core Fig. 2. Cross section of the power core segment generated by the ARIES systems code. 914 FUSION SCIENCE AND TECHNOLOGY VOL. 56 AUG. 2009

3 A cross-section of the tokamak power core generated by the systems code is shown in Fig. 2. The plasma contour is defined by the limiting flux surface. The contours of all the objects depicted are represented by the sequence of 2 nd order polynomials, which can be integrated to obtain volumes and cross-sections as needed. Costs of magnetic plasma confinement have a high impact on the cost of electricity, therefore toroidal and poloidal field magnets were modeled as accurately as the scope of the systems code allows. The corresponding algorithms are outlined in the following sub-sections. II.A.1. Toroidal Field Magnet Algorithm Toroidal field (TF) magnet consists of 16 coils of constant width and has a shape composed of two semi elliptic profiles that are joined at the vertical axis. A portion of the inner profile is flattened in order to allow for placement of the bucking cylinder and the central solenoid. Composition and thickness of the TF coil are determined by the specified toroidal magnetic field at plasma major radius and by the structural support needed to keep the magnet intact. Cable-in-Conduit Conductor is used with the nominal electric current of 40 ka. The CICC are embedded into a coil casing made of Japanese austenitic steel with low carbon and boron (JK2LB), suitable for a steady state machine with low cycling. The strands are composed of low temperature superconductor (Nb 3 Sn), stabilizer (Cu), with a diffusion barrier between the aforementioned components and coating. The volumetric fractions in the CICC are determined from superconductor, protection, cooling and structure considerations. Current density in the stabilizer is for protection with an aggressive active dumping mechanism. The insulation and cabling are set to 10% of the cable and the cooling fluid volume. The thickness of the TF coil was approximated by scaling from the finite element analyses of the ARIES- AT 10. II.A.2. Poloidal Field Magnet Algorithm Poloidal field (PF) magnet consists of 36 coils; 8 of these are placed along the inner radius of the bucking cylinder and comprise the central solenoid, while the remaining coils are evenly distributed along the outer surfaces of the toroidal field caps. Location of the outmost coil is limited by the maintenance port opening. Thickness and composition of the PF coils are determined by a procedure similar to the one used for the TF magnet. The coil currents and their corresponding rates of change are calculated at the zero-flux state. The currents are then scaled from the zero-flux state to the given values of q 95 and plasma current. The maximum current in the PF coil is calculated by taking into account the flux swing required to ramp up the plasma current from zero to the value required for the given operating point. The amount of structure (SS316) needed is calculated based on the hoop stress limit. II.B. Power Flow The power flow schematic of the current steady state tokamak chamber model is depicted in Fig. 3. The fusion power is generated in the plasma and transmitted to the power conversion system via neutrons and alpha particles. The power from neutrons is directly absorbed by the first wall, blanket, divertor and the high temperature (HT) shield. As the neutrons penetrate these components, they decelerate to a stop, transferring their entire kinetic energy into the thermal energy of the liquid Pb-17Li, which serves as a coolant and a Tritium breeder. As a byproduct of breeding, an additional fraction of ~10% of the neutron power is transferred to the coolant. A portion of the power from the alpha particles is radiated from the plasma to the coolant circulating in the first wall and divertor while the remainder is conducted to the divertor coolant via charged particles. The thermal power collected within the Pb-17Li coolant is transferred to a high efficiency helium gas turbine which utilizes Brayton cycle 9. The gross electric power output from the Brayton cycle is reduced by the amount needed to operate the blanket and divertor coolant pumps, current drives and various auxiliary functions, such as maintaining the cryogenic temperatures of the magnets, etc. The remaining, net electric power is the output to the consumer grid. II.C. Costing In the ARIES systems code, the costing is handled in three stages. In the first stage, the cost of each power core element is determined. In the second stage, the sequence of costing accounts for the power plant is evaluated. In the final stage, the cost of electricity is calculated. The data structure Part, used for describing the power core elements defines all the properties needed in order to evaluate the cost. Geometrical contours are spatially integrated in order to obtain the volume of the entity such as the first wall, blanket, etc. Volumetric and density fractions are specified as input parameters. An arbitrary number of different materials can be used to define the material composition of an entity. The materials are defined by their densities, costs per unit mass and reference years for those costs. The final cost of the entity is determined by summing up the costs of the all components. The revised costing account structure is shown in Table 1, where direct costs are represented by the accounts and indirect costs by the accounts Cost of electricity (COE) is the final output from the costing algorithm. FUSION SCIENCE AND TECHNOLOGY VOL. 56 AUG

4 Fig. 3. Power flow in a steady state tokamak. Table I. Revised Costing Account Structure (Values Given for ARIES-AT in 2008 dollars) Direct Costs M$ % Indirect Costs M$ % 20. Land and Land Rights 21. Structures and Site Facilities 22. Power Core Plant Equipment 23. Turbine Plant Equipment 24. Electric Plant Equipment 25. Heat Rejection Equipment 26. Misc. Plant Equipment 27. Special Materials 90. Direct Cost , , Construction Services and Equipment 92. Home Office Engineering and Services 93. Field Office Engineering and Services 94. Owner's Cost 95. Process Contingency 96. Project Contingency 97. Interest During Construction 99. Total Cost , III. RESULTS The systems code was validated against the ARIES- AT baseline. The costing of the ARIES-AT power plant with the new systems code and the relative departure from the published report 3 are summarized in Table 1. The present (2008) estimate of the cost of electricity for the ARIES-AT is mill/kwh, which differs by 2.4% from the inflation adjusted report in Ref. 3. A detailed comparison between the reference costing accounts and the new algorithm will be provided in the subsequent publication. Dependence of cost of electricity on the plasma major radius and toroidal field at plasma major radius is shown in Fig. 4. The lowest costs of electricity are connected into an optimal COE surface and the distribution of β n is shown as contours across this surface. The data visualization points to a region of attractive tokamaks, with low COE, compact size and high β n. Fig. 4. Cost of electricity and normalized beta versus plasma major radius and toroidal field at plasma major radius. ARIES-AT data point is provided as reference. 916 FUSION SCIENCE AND TECHNOLOGY VOL. 56 AUG. 2009

5 An alternative way to visualize the most interesting tradeoffs is depicted in Fig. 5. In this case, the design points are scattered in the parametric space of volumeaveraged plasma temperature and volume-averaged electron density. The cost of electricity that corresponds to each design point is color coded and shows a strong dependence on the electron density. A region of power plants with inexpensive electricity can be found around 20 the densities of 210 m -3 and temperatures between 15 and 25 kev. IV. CONCLUSIONS The new ARIES systems code is being developed as a tool for identifying the critical areas of research and development needed in order to advance from experimental tokamak facilities to commercial power plants. In order to achieve this goal, the systems code is equipped with a physics algorithm that accurately describes high energy tokamak plasma, engineering algorithm that reflects the advanced technology of the power core with ancillary systems and costing that fully estimates the impact of these technology solutions. Parametric scan through a wide design space around the well researched solutions such as ARIES-AT provides a rich database of operating points which shows that sizable regions of economically attractive machines can be found. This database can be explored by modern techniques such as data mining in order to provide the knowledge on key tradeoffs in design parameters that may yield a highly acceptable commercial power plant. A more in-depth analysis will be provided in subsequent journal publications. Fig. 5. Volume-averaged temperature versus volumeaveraged density. Cost of electricity is shown as contour plot in 2008 dollars. REFERENCES 1. D. A. DEFREECE, G. R. FULLER, L. M. WAGANER, "Impact of Confinement Physics on Reactor Design and Economics", 7th Symposium on Engineering Problems of Fusion Research, Knoxville, TN, October McDonnell Douglas Astronautics Company - East. 2. J. G. DELENE, R. A. KRAKOWSKI, J. SHEFIELD, R. A. DORY, GENEROMAK Fusion Physics, Engineering and Costing Model, Oak Ridge National Laboratory Report, ORNL/TM (1988). 3. F. NAJMABADI and the ARIES Team, The ARIES-AT Advanced Tokamak, Advanced Technology Fusion Power Plant, Fusion Engineering and Design, 80, 3 (2006). 4. M. E. FENSTERMACHER, MUMAK A Computer Code for Modeling Plasma Power Balance and Current Drive in Tokamaks, Lawrence Livermore National Laboratory Report UCID-21038, April W. M. STACEY, V. A. MARONI, J. R. PURCELL, et al., Tokamak Experimental Power Reactor Studies, Argonne National Laboratory Report ANL/CTR-75-2 (1975). 6. P. I. H. COOKE, R. HANCOX, W. R. SPEARS, Parameters of a Reference Tokamak Reactor, UKAEA Culham Laboratory Report CLM-R298 (1989). 7. R. HIWATARI, K. OKANO, Y. ASAOKA, K. SHINYA, Y. OGAWA, Demonstration Tokamak Fusion Power Plant for Early Realization of Net Electric Power Generation, Nuclear Fusion, 45, (2005) C. E. KESSEL, D. MEADE, D. W. SWAIN, P. TITUS, M. A. ULRICKSON, Advanced Tokamak Plasmas in The Fusion Ignition Research Experiment, 20 th IEEE/NPSS Symposium on Fusion Engineering, San Diego, October R. RAFFRAY, L. EL-GUEBALY, S. MALANG, I. SVIATOSLAVSKY, M. S. TILLACK and the ARIES Team, Advanced Power Core System for the ARIES-AT Power Plant, Fusion Engineering and Design, 80, 79 (2006). 10. F. DAHLGREN, T. BROWN, P. HEITZENROEDER, L. BROMBERG and the ARIES Team, ARIES-AT Magnet Systems, Fusion Engineering and Design, 80, 139 (2006). ACKNOWLEDGMENTS This work was supported by the United States Department of Energy, Office of Fusion Energy DE- FC03-95ER FUSION SCIENCE AND TECHNOLOGY VOL. 56 AUG