paper nafems final1

8/3/2019 Paper NAFEMS Final1

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SIMULATION OF COMPLEX NON-LINEAR STRUCTURES IN

LARGE SCALE ANALYSIS

technically 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 0.6m (Fig. 2). By reason of thesmall 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 initiate a so called quench

(loss of the superconducting properties) 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 reliable predicted by means

of extensive finite element (FE) analyses only. The principal aim of structural

analysis is to create a global model of the experimental device and additionallya majority of sub-models for each system and 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 the confidence on the

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

1: Introduction

The plasma fusion research is focused world wide 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 (IPP). 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 (Fig. 4). 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 coils types only. The coils are

arranged toroidally inside a cryostat which has an average large diameter of


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11m. The 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 build 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 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 by the introduction of

special boundary conditions and consists of 5 MF and 2 AF coils (Fig. 5). This

is possible because the original geometry as well as 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 very carefully -

taking into account all essential physically and geometrically 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 special 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 (Fig. 5) 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 manly 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 segment of the coil

a.) b.)


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housing), the intermediate joints, realized by contact elements, are balancing

the forces between two adjacent coils.

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

intermediate joints, so called lateral support element (LSE), are responsible for

the stabilization of the equilibrium of the coil arrangement in lateral direction.

The housings of the AF coils are fixed to the central support ring at two

locations in a similar way like MF coils. Additionally, these AF coils are fixed

laterally at both sides. 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. The counter part of the lateral

fixation, called planar support elements (PSE), is constrained to the housings of

the MF coils. Additional contact elements (CE) positioned at the top and

bottom side of the coils in the half module symmetry surface increase the

lateral stiffness of the coil arrangement additionally. The coil housing

connection of the both MF and AF coils to the support ring (via CSE) has been

realized using a bolted connection (Fig 9). Due to the geometrical

requirements, the CSE consist of 2 separated parts, one belongs to the coil

housing and the other one to the support ring. This involves some additional

investigations of the connecting elements.

3: Benchmark analysis results

The ADINA [5, 6] code has been used for the present benchmark analysiswhereas the ANSYS [7] code has been used for the long-term analysis. The

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 MeshContinuity

Discontinuous Continuous

NSE Geometry Definition Approximately CAD-Model complying

Bolt and Pin Distribution

(Planar Coils)Approximately CAD-Model complying

Solution Contact Algorithm Penalty Method Constraint Function


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Model Mesh Size Totally 360000 Elements 340000 Elements

Because of the necessity to make the results of both models comparable, the

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

36 model, conditions like cool down and gravitational forces are neglected.

A first information of 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 of 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 by the ADINA model 18.66 mm and by

the ANSYS model 16.5 mm.

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 e.g. 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 e.g. 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 a very strictly criterion too, for the confidence to the results of the

benchmark analysis. The result values vary with a slightly 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 show sufficient agreement. For the

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

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

correspondent 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, the contact property definition in the models have been done by a

different way also. 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 definition, 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 the

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

be within 30%.

Additionally to the above described benchmarking, the ADINA global

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

detailed analysis of all NSEs was not possible in global model of the long-

term analysis. This part of the analysis has been done by means of trials for

a particular element and a particular load as a worst case analysis.

Correspondingly, the model can be used for an additional result evaluation

like contact surface pressure, contact surface area in contact, contactslipping, 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 9 and 10 show an example of contact surface

pressure and contact surface sliding for an individual narrow support

element between coil housing 1 and 50.


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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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