Development and Scope of ARIES Systems Code

Zoran Dragojlovic A. René Raffray

Farrokh Najmabadi

ARIES-“TNS” Project MeetingApril 3 and 4, 2007

University of California in San Diego

Purpose of Code• To allow the possibility of a wide trade-off study while using the

actual design points instead of “fudge factors”.• In the ARIES Next Step project, this code will help establish a

database to understand impacts of different physics and technology on a prototypical power plant so that necessary assessments can be made.

• Previous code was built layer-by-layer until it became too cumbersome to be used for an effective study. Major shortcomings include:– Optimization process was not transparent, the final answer was

sometimes hard to explain or justify. – Inaccurate geometry.– Lack of user-friendly pre and post processing interface.– Lack of documentation.

• We are building a new ARIES systems code.– Programming is being done “from scratch”, as opposed to building on

top of the existing code.– Initially, we may borrow parts of the existing code that are correct, such

as the costing algorithms but a different optimization process will be employed.

Requirements

• Transparent system optimization that shows trends instead of single data points.

• Lean and time efficient processing.• Total CPU time per optimization case should be

reasonable (~30 min, for example).• Accurate geometry with adjustable resolution.• Easy to use pre and post-processing

interface.• Ample amount of documentation (manual,

comments within the code, etc.)

The Systems Analysis Approach

– Sequential loops will be implemented instead of nonlinear search.

• Physics. – Plasma shapes and parameters from a wide range of possible operating

points will be provided in order to calculate the wall loads. Data will be based on Fusion Ignition Research Experiment (FIRE), PPPL.

• Engineering. – Inboard radial build based on the wall loads, primarily due to neutrons.– Outboard radial build is based on engineering and maintenance

requirements.– Power flow– Implement example configurations based on past studies for more efficient

programming

• Costing Analysis.– Initially, the costing algorithms will be implemented from the previously used

ARIES systems code.– Costing accounts will be modified, as needed.

Pre-Defined Example Configurations

• The pre-defined configurations, A, B, C, etc. will be based on past studies and will allow a “plug and play” mode of use for more efficient analysis.

BlanketA radial build

……

…Power

…

………

B

C

ShieldA radial build

……

…Power

…

………

B

C

DivertorA radial build

……

…Power

…

………

B

C

CoilA radial build

...…

…Power

…

………

B

C

Responsibility and Scope

• 3 year ARIES Next Step Project and beyond.

Physics Charles Kessel Princeton Plasma Physics Laboratory

Systems Code +Engineering

Zoran DragojlovicRené RaffrayFarrokh Najmabadi

University of California in San Diego

Costing Analysis + Engineering

Laila El-Guebaly University of Wisconsin

Costing Analysis Lester Waganer The Boeing Company

Magnet Algorithm Massachusetts Institute of Technology

Current Accomplishments

• 3-D TOKAMAK geometry is built. Various spatial integrals such as volumes and areas of different parts can be evaluated, as needed for the engineering and costing analysis.

• Implemented a power flow scheme.• All the relevant algorithms are written in

Fortran. The graphic representation of data is generated by using a suite of Matlab scripts (single command).

Choice of a Programming Language

• Benchmark reports of 2004 and later indicate that the two competing languages of choice for numerical computing are still Fortran and C++.

• There are three possible choices: using Fortran only, using C++ only and combining Fortran and C++. Both languages are suitable for the purpose, portable and can make user friendly applications.• Fortran Only:

• Fastest for numerical computing in general.• Superior handling of numerical arrays.• When the Fortran code is optimized for performance, it looks simpler and

easier to understand than when C++ is optimized for performance.• Easy to link with other relevant codes that are also written in Fortran.

• C++ Only:• Latest brands of compilers are almost as fast as Fortran. • Perceived to be a more modern language, popular among computer

scientists as a tool for programming operating systems.• Fortran & C++:

• Use C++ for handling data structures and dynamic memory allocation.• Use Fortran for all numerical computations.• I already have experience employing this strategy in SPARTAN.

Geometry

• Started from the plasma shape as a reference point, built the geometry around it by using ARIES-AT CAD drawings and radial builds from design book.

• Tested the geometry for random variations in plasma shape to make sure that everything fits together.

• Tested the volumes and surface areas of the ARIES-AT power core by comparison with the Pro-E values from design book.

ARIES-AT Geometry Generated by Systems Code

Examples of Geometrical FeaturesMaintenance Port

Detail of Divertor Region

The new systems code generates geometry that is truly 3-D. An example is the maintenance port, shown above.

Divertors are represented by Bezier curves, which allows the user to prescribe an arbitrary angle between the divertor and the last closed magnetic surface.

Arbitrary gaps between adjacent parts are allowed.

Power Core Volumes and Surface Areas Match the ARIES-AT Design Book Values (Pro-Engineer)

VolumesDesign Book [m3]

New Systems

Code [m3]

Error Relative to

Design Book [%]

Plasma 308.219 309.543 0.43Blankets 17.58 18.681 6.26Shield 8.1 8.173 0.91Divertor 1.7 0.799 52.98Power Core Sector

29.86 27.654 7.39

Surface Areas

Design Book [m2]

New Systems

Code [m2]

Error Relative to

Design Book [%]

First Wall 354.4 367.402 3.67Divertor

–Inboard 40.9 41.979 2.64–Outboard 54.9 56.03 2.06–Dome 50.8 55.539 9.33

•Total Div. 146.6 153.548 4.74

CAD Drawing

Systems Code

Power Flow

• Power flow algorithm was implemented simultaneously with geometry. ARIES-AT design study was used as a model.

• Efficiency of the Brayton cycle is estimated based on the average neutron flux on the first wall.• The flow chart is generated automatically by a Matlab script.

[MW]

PNDD – power from neutrons in D-D reaction.

PNDT – power from neutrons in D-T reaction.

PCP – charged particle fusion product power.

A Simple Optimization Test• This test was done in collaboration with Charles Kessel, PPPL. The

motivation was to incorporate the new geometry into the existing physics and engineering codes and make a step beyond testing surface areas and volumes against the ARIES-AT design book.

• Test runs:• Charles Kessel:

– Generated 165,000 physics operating points close to ARIES-AT specs.

– Assembled a code that tests the operating points for engineering limits, such as:

» first wall heat flux » divertor peak heat flux » TF peak field limit/superconducting current density limit » bucking cylinder criteria » PF coil peak field/superconducting current density limit » resulting inboard radial build with assumed thicknesses for the

FW, blanket, shield, and VV from ARIES-AT neutronics analysis.– Final outcome: 120 data points that survived all the engineering limits.

• Zoran Dragojlovic:– Generated geometry for the 120 data points, eliminated 23 points

based on geometry. – For the remaining points, used the power flow algorithm to estimate the

trends that maximize the net electric power.

Input Data for Geometry and Power Flow Algorithms

• 120 data points with 83 different parameters describing – Plasma shape and physics.– Inboard radial thicknesses.– Electrical and magnetic data

for coils.– Power distribution with electric

power as a final outcome.• Parameters I used as input

are:– Plasma shape ( 5.1 m ≤ R ≤

7.8 m, 1.275 m ≤ a ≤ 1.95 m).– Inboard radial thicknesses.– Fusion power (2.137 GW ≤

Pfusion ≤ 2.175 GW).

= 0.7

Optimization Based on Trends in Net Electric Power

“level 1”

“level 2”

“level 3”

“level 4”A fictitious cost of electricity distribution.

Possible optimal solution.

A single optimal data point as a possible outcome of nonlinear search.

CO

E (f

ictit

ious

)

• The net electric power was estimated by the new power flow diagram. The values are within 4-5% from those provided by Chuck Kessel.

• The data points were then ordered in the increasing sequence based on the net electric power. The diagram above indicates the existence of 4 distinctive groups or “levels” with low variations of power within each group.

• The fictitious cost of electricity distribution is drawn above to illustrate the need for understanding trends within similar solutions (such as the one marked as “level 3”) instead of using a single optimal data point.

Variation in Geometry Within the Range of Optimal Solutions (“level 3”)

• Group of data points with similar net electric power (“level 3”) allows for a variety of different chamber sizes.

R = 5.4 m

R = 7.2 m

a = 1.35 m

a = 1.8 m

Comparison Between Levels 3 and 4

• Both groups of data points feature the same variation in plasma size. However, most of the data points in the lower electric power group (level 3) have the major radius of 7 m or larger. In the higher electric power group, on the other hand, most of the data points are under 6 m in the major radius.

• This observation serves as an example of how optimization can be formulated to identify trends within similar solutions instead of single point outcomes of nonlinear search.

Level 3: Pnet electric = 955 MW

Level 4: Pnet electric = 960 MW

Plan of DevelopmentDeliverables Criteria of Success Duration Date

ExpectedEngineering Algorithms

•Radial and vertical builds implemented.•Pre-defined example configurations for blanket, shield, divertor and coil available.

2-3 months

June 2007

Costing Algorithms(simultaneously with engineering algorithms)

•Costing algorithms extracted from the previous systems code, verified and implemented.

2-4 weeks

June 2007

Test for Cost of Electricity

•Ability to compare the results from the new and old systems code. Discrepancies are expected, within reason. A huge discrepancy would indicate a possible error in the new algorithm.

1 month July 2007

Conclusions and Discussion• Development of the ARIES systems code is

gaining momentum, as demonstrated today.• Initial achievements include:

– Accurate geometry, with the resolution that can be adjusted to fit the needs of the analysis.

– Power flow diagram is available as the first stage of implementation of the engineering algorithms. Radial and vertical build are expected in the near future.

– Geometry and power flow diagram can be integrated to perform a simple optimization, as shown in the example with data from Chuck Kessel.

• We have suggested the basic requirements for the code and set the milestones in the algorithm development. Both are open for discussion.