Paper N.jaksic

8/3/2019 Paper N.jaksic

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SIMULATION OF COMPLEX NON-LINEAR STRUCTURES IN

LARGE SCALE ANALYSIS

SIMULATION OF COMPLEX NON-LINEAR STRUCTURES

IN LARGE SCALE ANALYSIS

Nikola Jaksic, Jochem Simon-Weidner, Felix Schauer, Paul van Eeten,

Manfred Sochor

Max-Planck-Institute for Plasma Physics, Germany

THEME

Confidence in Engineering Analysis Results

KEYWORDS

Structural Analysis, Benchmark, Superconducting Coils, Fusion, Stellarator.

SUMMARY

A large steady-state plasma fusion experimental device of the stellarator family

is being developed at Max-Planck-Institute for Plasma Physics (IPP), branch

institute Greifswald Germany. The ultimate aim of fusion development (R&D)

work is to make fusion energy usable for energy supply, mainly for providingelectrical energy. The fundamental principle of the energy extraction by fusion

is based on fusion of light atoms (e.g. hydrogen isotopes) in a very hot gas

(plasma) which is confined by a strong magnetic field. The magnetic field is

generated by superconducting coils which produce the magnetic induction of

3T at the centre of the plasma column [3]. In order to ensure the precise

localisation of the magnetic field confining the plasma, the central pathway of

each of the individually shaped coils should be predictable during operation

with high accuracy. In relation to the size of the complete experiment of

roughly 15 m (total diameter), the required position accuracy of the main

components is in the range of 1.0- 2.0

10

3

. An important characteristic ofthe magnet coil structure is the multiple interior symmetry conditioned by

physical demands. Additionally to the positioning tolerances, angle tolerances

of 0.5 are prescribed to reduce the deviation of axial symmetry. The

superconducting magnets have to be kept at cryogenic temperature (4K).

Next important characteristics of the experimental device are the extremely

high temperature differences within the structural elements, which are partly

very close to each other. Some parts of the plasma surrounding structure are


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locally loaded by a power of 10 2/mMW . E.g. it is a big physical and

technical challenge to design a thermal insulation for a device with central

temperatures in the range of 100 mill. K (plasma column centre) and 4 K(superconducting coil) with a distance of about 0.6 m (Fig. 1, 2). By reason of

the small distance between the structural elements (< 10 mm) with a

temperature difference of about 300 K, it is important to avoid a contact

between the elements during operation. A contact of structural elements with

different temperatures causes high cryogenic losses and could impede proper

operation of the superconducting coils. Therefore, it is necessary to predict the

element position during operation as precise as possible.

The behaviour of such a complex structure can be reliably predicted by means

of extensive finite element (FE) analyses only. To this end it is essential to

create a global model of the experimental device, and additionally a number ofsub-models for each system and in particular the critical components. The

global model has been extensively used for mechanical and thermal analyses

[2]. These analyses have shown that the structure reacts highly sensitive onto

changes of initial contact gap widths, contact friction factor and other

parameters like bolt pretension, general coil stiffness definition, etc.. The main

reasons for the high sensitivity of the structure are multiple internal

geometrical nonlinearities.

As a consequence, it has been decided to perform a benchmark analysis with an

entirely independent FE model with the aim to increase confidence in the

analysis results. The benchmark analysis procedure is the main subject of thispaper.

1: Introduction

The plasma fusion research is focused worldwide on two different types of

experimental devices tokamak and stellarator with different principles of

plasma confinement. The world's largest plasma fusion experimental device of

the stellarator type, called Wendelstein-7X (W7-X, Fig. 1), is presently being

built at the Max-Planck-Institute for Plasmaphysics. The aim of the experiment

is to prove the reactor validity of the stellarator research line in addition to the

tokamak research line. The inherent property of the stellarators is a true steady

state operation which is of major interest for fusion reactors.

The superconducting magnet system with the support structure represents the

core of the device and will be the main subject. The important characteristic of

the magnet geometry is the five-fold symmetry and the modularity of the coil

arrangement system. The coil system consists of 50 module field coils (MF)

and 20 ancillary field coils (AF). Due to symmetry conditions within a module,

there exist five MF and two AF coil types only. The coils are arranged

toroidally inside a cryostat which has an average large diameter of 11 m. The


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MF coils are wound with 6, the AF coils with 3 double layers of a cable in

conduit conductor, which is cooled by forced flow supercritical helium at a

temperature of approximately 4 K.

Figure 1: Assembly of the fusion experimental device W7-X, a birds eye view

Figure 2: Cross-

Section

through

the

experimental device,0

0=


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Figure 3: Assembly of a superconducting magnet coil W7-X

The cable is built by 243 NbiTi/Cu strands which are enclosed by an

aluminium alloy jacket (16 x 16 mm), shown in Figure 3. The winding pack by

itself is not strong enough to withstand the high electromagnetic forces [4].Therefore, individually adapted coil housings (e.g. the cast steel 1.3960) with

sufficient cross section have to be designed to encapsulate the windings and to

support the remaining integral forces. The embedding of a quartz sand-armed

resin guarantees a gap-less transmission of the electromagnetic forces of the

superconducting strands through the conductor jackets via the basic insulation

to the coil housing. The considerable residual forces of the modules have to be

balanced: First by a central support ring, secondly by lateral support elements

between the coils and thirdly by additional lateral pads near the inside

circumference of the coil set. The main features of the superconducting coil

system (Fig. 4) are summarized in Table 1.

Table 1: W7-X - coil system parameters

Number of module field coils (MF) 50

Number of ancillary coils (AF) 20

Main radius of module field coils 1.5 m

Min. distance plasma-coil 0.3 m

Max. current in the conductor 18.2 kA

Max. magnetic induction on axis 3.0 T

Max. magnetic induction at the coil 6.7 T

Max. stored magnetic field energy 0.62 GJ

Time for discharge of magnetic energy 5 s

Max. force on a coil 3.76 MN

2: Description of the FE-Model

2.1: General

The FE-model is reduced to 1/10th of the whole system, consisting of 5 MF

and 2 AF coils, by introduction of special boundary conditions (Fig. 5). This is

possible because the original geometry as well as the loading of the structure


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obey specific symmetry properties. The derivation of the special symmetry

definition is described detailed in [1]. Neglecting the influence of gravity, a 36

sector model can be built using these boundary conditions. Considering thegravity, an extension to a 72 sector model has to be realized.

Figure 4: Coil arrangement of fusion experimental device with axes of symmetry

2.2: FE-Model Preparation

The FE-Model for the benchmark analysis has been done by taking into

account all essential physical and geometrical features of the structure as

accurate as possible keeping in mind the global model size. Here some

examples:

Modelling of geometrical nonlinearities contact surfaces

Modelling of structural junction elements bolts, weld seams

Modelling of specially shaped contact surfaces spherical

interface boundary surface

Taking into account different material and frictional properties


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Figure 5: FE-Model of fusion experimental device top view

Figure 6: Suspension of the coil casing 1 on the support ring side view to the coil


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Figure 7: Discretization of the coil cross-section a.) MF-coil and b.) AF-coil

Figure 8: Narrow Support Element Figure 9: Central Support Extension

(Cross-Section) (Cross-Section)

Table 2: FE-Model main parameters

Node number 368369

Element number 340000

Number of contact surfaces pairs 11

Number of contact surfaces 104

Number of contact segments 100000

The general principle of the coil support structure (Figs. 5, 6 and 7) is: Each

particular coil housing is fully separated from each other and has to carry the

primary load caused by electromagnetic forces due to the current of the coils

within the magnetic field. The toroidal arrangement of the MF coil housing is

fixed to the central support ring with special joints, called central support

elements (CSE), at two locations (Fig. 6) only. Additionally, a mutual support

between adjacent coil housings is realized by intermediate joints which are

mainly loaded by compressive loads. These intermediate joints (located at

different positions at the circumference of the coils) are operating with

different functions: At the regions of small distances between the coils (internal

a.) b.)


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segment of the coil housing), the intermediate joints, realized by contact

elements, are balancing the forces between two adjacent coils.

These intermediate joints, so called narrow support elements (NSE), (Fig. 8)have an essential effect on the lateral stiffening of the structure. Other

intermediate joints, so called lateral support elements (LSE), are mostly

responsible for the stabilization of the equilibrium of the coil arrangement in

lateral direction. The LSE elements at the module symmetry surface ( =0 )

and the half module symmetry surface ( =36 ) stabilize the relative shear

movement of the coil housings considerably. The housings of the AF coils are

fixed to the central support ring at two locations in a similar way like the MF

coils. Additionally, these AF coils are fixed laterally at both sides to the MF

coils via so called planar support elements (PSE). This fixation is realized

using the contact surface capability so that the radial displacement (viewed in

local coordinate system of the coil) is performed without constraints.

Additional contact elements (CE), positioned at the top and bottom side of the

MF coils in the half module symmetry surface, increase the lateral stiffness of

the coil arrangement. The coil housing connections of the both the MF and AF

coils to the support ring (via CSE) have been realized using bolted connections

(Fig 9). Due to their complex geometry and the enormous loads they require

special investigations.

3: Benchmark analysis results

The ADINA code [5, 6] has been used for the present benchmark analysis,whereas the ANSYS [7] code is the workhorse for the W7-X structural analysis

in the long term. Most important differences in the model definition are

summarized in table 3.

Table 3: Main models definition differences

ANSYS ADINA

General Mesh Definition

inside of Solids Mesh

Continuity Discontinuous Continuous

NSE Geometry Definition Approximately complying with CAD-Model

Bolt and Pin Distribution

(Planar Coils)Approximately complying with CAD-Model

Solution Contact Algorithm Penalty Method Constraint Function


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Model Mesh Size Totally 360000 Elements 340000 Elements

Due to the fact that the results of both models have to be comparable, the

general boundary conditions for bothFE-Models have been mutually agreed,and the so called Low-Iota load case has been applied to the 36 model.

Conditions like cool down and gravitational forces are neglected.

First information on the behaviour of the structure for a particular boundary

conditions case is given by the result of the displacements (Fig. 10).

Figure 10: Displacement Magnitude from ADINA Model Top View

The comparison of the displacements given by the ANSYS code shows

similar values. Nearly the same displacement pattern could be found withinthe whole structure in both cases. The maximum displacement (limited on a

small quite sensitive area) amounts 18.66 mm by the ADINA model and

16.5 mm by the ANSYS model.

The next step in the benchmark analysis belongs to the comparison of the

cross-sectional forces and moments for the most stressed structural

elements like CSE and LSE. By reason of comparison, the cutting surface

for the evaluation of the cross-sectional loads has been exactly predefined.


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The notation in the table 4: NPC1Z1 means central support extension at

coil 1 upper and NPC1Z2 means central support extension at coil 1

lower, etc..

Table 4: Cross-Sectional Forces at CSE

ANSYS ADINA ANSYS ADINA ANSYS ADINA

CSEFx Fx dev Fy Fy dev Fz Fz Dev

MN MN % MN MN % MN MN %

NPC1Z1 0,714 0,714 0,0% 0,259 0,177 5,9% 1,214 1,082 9,6%

NPC1Z2 -3,146 -3,317 5,2% 0,242 0,189 1,6% -0,707 -0,568 4,2%

NPC2Z1 -0,764 -0,896 9,6% -0,332 -0,431 7,2% 1,015 1,050 2,5%

NPC2Z2 -0,651 -0,605 3,7% -0,002 -0,074 5,8% -1,079 -1,073 0,5%

NPC3Z1 -1,021 -1,047 2,2% 0,186 0,080 8,7% 0,617 0,635 1,4%NPC3Z2 -2,080 -2,088 0,3% 0,614 0,661 2,0% -0,909 -0,888 0,9%

NPC4Z1 0,130 0,161 3,6% -0,036 -0,007 3,4% -0,861 -0,830 3,5%

NPC4Z2 -2,016 -2,022 0,3% 0,106 0,014 4,3% -0,746 -0,841 4,4%

NPC5Z1 0,055 0,082 3,4% -0,703 -0,754 6,3% -0,375 -0,355 2,5%NPC5Z2 1,446 1,578 8,7% -0,097 -0,106 0,6% -0,090 -0,119 1,9%

Table 5: Cross-Sectional Forces at LSE

ANSYS ADINA ANSYS ADINA ANSYS ADINA

LSEFx Fx dev Fy Fy dev Fz Fz dev

MN MN % MN MN % MN MN %

LSE1-1 0,305 0,277 2,0% 1,032 0,933 7,0% -0,983 -0,964 1,3%LSE1-2 0,344 0,327 1,9% 0,402 0,342 7,1% 0,665 0,716 6,0%

LSE2-3 0,304 0,302 0,5% 0,266 0,233 6,8% 0,277 0,294 3,5%

LSE3-4 0,080 0,095 2,1% 0,703 0,686 2,5% -0,043 -0,073 4,2%

LSE4-5 -0,886 -0,936 3,6% 1,055 1,088 2,3% 0,087 0,068 1,4%

LSE5-6 -1,058 -1,069 0,8% 1,030 1,082 3,5% 0,134 0,142 0,6%

The notation in the table 5: LSE1-1 means lateral support element

between coil type 1 and 50 and LSE1-2 means lateral support element

between coil type 1 and 2, etc..

The comparison of cross-sectional forces and moments is very important

and also a very strict criterion for the confidence in the results of the

benchmark analysis, too. The result values vary with a slight position

change within the area of interest. The fineness and the style of the mesh

might influence the results as well. Nevertheless, the comparison of the

cross-sectional forces and moments shows sufficient agreement. For the

comparison only the significant values of the results have been taken.

Values with low contribution have been neglected by reason of relevance.

The comparison of the cross-sectional forces (Tables 4 and 5) show a total

maximum deviation of less than 10%. The maximum deviation of

corresponding cross-sectional moments has been found to be within 30%.


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Furthermore, the contact forces at the NSEs have been compared as well.

Note that the contact property definition in the models has also been done

in a different way. Moreover, the FE models use different contact solutionalgorithms (Table 3) to solve the contact problems.Table 6: Contact Forces

ANSYS ADINA

Pads Fx Fx dev

MN MN %

50E2--> 1E2 0,692 0,624 10,2%

In spite of entirely different contact definitions, the contact forces are in

good agreement as well. The example in table 6 for the contact surfaces

between the coils 1 and 50, which are representative for relevant values,

shows a contact force deviation of about 10%. A maximum deviation of

contact forces for contact surfaces with fewer relevancies has been found to

be within 30%.

In addition to the above described benchmarking, the ADINA global model

allows also an advanced analysis of all narrow support elements. Such a

detailed analysis of the NSEs within the global model was not possible

with the ANSYS model. It has been realised by means of trials and local

models for a particular element and a particular load as a worst case

analysis. Correspondingly, the ADINA model can be used for an additionalresult evaluation like contact surface pressure, contact surface area during

operation, contact slipping, etc.. A confident analysis for narrow support

element results is extremely important for the reliability of the whole

device since these elements are the most stressed elements in the structure

with loads at the mechanical limit. Figures 11 and 12 show examples of

contact surface pressure and contact surface sliding for an individual

narrow support element between coil housings 1 and 50.


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Figure 11: Contact Surface Pressure Figure 12: Contact Surface

Sliding

The notation in the figures 11 and 12, NPS1E8-NPS50E9, denotes a

contact surface pair between coil casing 1 and 50.

4: Conclusions

This paper describes the first step of a large scale benchmark analysis for the

complex structure of the W7-X fusion experimental device. After additional

improvements of the 36 benchmark model, the computing will be expanded to

a 72 model. The present benchmark analysis has been done by comparison of

the results of two FE-Models which have been modelled independently of eachother. The finite element analysis has been done by different FE codes as well.

In the present case the ANSYS code is the main analysis tool in the long term,

whereas the ADINA code is being used for the present benchmarking. The

comparison of the results of the benchmark analysis shows a maximum

deviation of 2.0 mm for displacements with a maximum value of 18.7 mm.

Furthermore, the comparison of the cross-sectional forces and moments and the

comparison of the contact forces show sufficient agreement. All results of the

benchmark analysis show values within the expected limits, i. e. they are

within 10% for the critical components and 30% for the non-critical ones.

However, all these results lie within the safety margin defined for the W7-X

structural analysis. In such a complex and multiple nonlinear structure, the benchmark analysis is the basis to get confident results since actual

experimental values are not available.

REFERENCES

1.Jaksic N. et al., Definition der Randbedingungen bei einer FE-

Strukturanalyse durch Nutzung Symmetriebedingungen einer

Stellarstoranordnung, IPP/Z3, february 1997


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2.Bykov V. et al., Structural analysis of W7-X: Main results and critical

issues, Fusion Engineering and Design 82 (2007), pp. 1538-1548.

3.Jaksic N. et al., Design analysis of the support structure stressed by large

superconducting coils for a plasma fusion experiment, Computers &

Structures 81 (2003) pp.697-714

4.Simon-Weidner J. et al., On mechanical stress in large helias coil systems

and the influence of contact effects, proceedings of the 16th SOFT,

London, (UK), 3-7 September 1990, pp. 1511-1514.

5.Bathe K. J., Finite Element Procedures, Prentice Hall, Upper Saddle

River, NJ 07458, 1996.

6.ADINA R&D Inc., A finite element computer program for Automatic

Dynamic Incremental Nonlinear Analysis - System 8.5, 71 Elton

Avenue, Watertown, MA 02472 USA, 2001.

7.ANSYS, Engineering Analysis System, Release 10.0A1, ANSYS Inc.

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