study of radiation heat transfer between pfc and vacuum vessel during sst-1 baking

Technical note

Study of radiation heat transfer between PFC and vacuumvessel during SST-1 baking

Paritosh Chaudhuri *, D. Chenna Reddy, P. Santra, S. Khirwadkar,N. Ravi Pragash, Y.C. Saxena

Institute for Plasma Research, Bhat, Gandhinagar 382 428, India

Received 25 October 2001; received in revised form 27 February 2002; accepted 1 May 2002

Abstract

Steady-state superconducting tokamak (SST-1) is a medium size tokamak with superconducting magnetic field coils.

Plasma facing components (PFC) of SST-1 are placed inside the vacuum vessel (VV) of the tokamak and are designed

to be compatible for steady-state operation. The main consideration in the design of the PFC is the steady-state heat

removal of upto 1 MW/m2. In addition to remove high heat fluxes, the PFC are also designed to be compatible for

baking at high temperature. Since it is difficult to calculate the radiation heat loads between PFC and VV in a 3-D

irregular geometry, a simplified model of concentric cylinders has been chosen for the purpose of estimation of the

power requirements and the thermal responses of PFC and VV during their bakeout phases. Thermal responses of the

PFC and VV have been analysed and the analytical results have been compared with 2-D finite element analysis using

ANSYS. The radiation losses between PFC and VV also have been evaluated on the actual model containing all PFC

inside the VV.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: Radiation; Radiative heat load; View factor; Baking; PFC; Vacuum vessel; Steady-state superconducting tokamak

1. Introduction

SST-1 tokamak is a superconducting steady-

state tokamak designed for plasma discharge

duration of �/1000 s to obtain fully steady-state

plasma [1]. Plasma facing components (PFCs), one

of the subsystem of SST-1, consisting of divertors,

passive stabilisers, baffles and poloidal limiters are

designed for the intended long pulse, double null

plasma operation [2]. Except the poloidal limiters

all other PFC are structurally continuous in the

toroidal direction. For ease of assembly inside the

vacuum vessel (VV), the PFCs are designed to be

modular. An elevation view of SST-1, indicating

all PFC along with the main VV is shown in Fig. 1.

All the PFCs have the same basic configuration:

graphite tiles are mechanically attached to high

strength copper alloys, and SS tubes are brazed in

the grooves on the copper back plates as shown in

* Corresponding author. Tel.: �/91-79-396-9001x318; fax: �/

91-79-396-9017

E-mail address: [email protected] (P. Chaudhuri).

Fusion Engineering and Design 65 (2003) 119�/132

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0920-3796/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved.

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Fig. 2. The same tube will be used for dual purpose

of baking and cooling [3].

During the initial phase of operation of SST-1, it

is planned to bake the VV at 250 8C by flowing

hot nitrogen gas through the channels welded on

its inner wall and all PFC will be baked by

radiation from the heated VV wall. Even though

PFC is within the closed VV and will ultimately be

raised to the VV temperature, it is important to

know the thermal responses of the PFC during the

baking phase. If the thermal response is slow, then

alternative ways of heating the PFC may need to

be considered. During later phases of operation of

SST-1, if required, i.e. if 250 8C baking of PFC isnot sufficient to remove the impurities from the

PFC surfaces, the PFC will be baked indepen-

dently at 350 8C while maintaining the VV

between 150 and 200 8C. This will be done by

flowing hot nitrogen gas at about 400 8C inlet

temperature through the tubes embedded in the

backplates of the PFC. The details of the indepen-

dent baking of PFC is discussed in [4]. If the powerradiated by the PFC is more than the power

needed to maintain the VV at 150�/200 8C, the

VV need to be cooled. If the power is less, then

additional power needs to be supplied to the VV to

maintain that temperature. Thermal responses of

the PFC and VV during their bakeout phases have

been calculated analytically and 2-D finite element

(FE) analysis using ANSYS. Before attempting todo the analytical and FE solution for radiation

heat transfer between PFC and VV, a benchmark

problem of a concentric cylinder has been solved

which is discussed in detail in Ref. [5]. The

radiation losses between PFC and VV also has

been calculated on the full model containing all

PFC inside the VV. The details of the temperature

responses of PFC and VV and their respectiveradiative loads for simplified and full model during

baking are presented in this paper.

2. Objectives

The purpose of high temperature bakeout is to

clean the PFC surfaces to limit the flow ofimpurities into the plasma during operation. The

objectives of the radiated heat load calculations

are to find the transient and steady-state thermal

responses of PFC and VV and the radiation losses

between them during their bakeout phases. PFCs

are enclosed in the VV and form a toroidal

geometry whose major and minor radii are 1.1

and 0.2 m, respectively. The amount of radiatedpower loss between PFC and VV surfaces during

their bakeout phases depends on their temperature

and their mutual exposed area. Surface radiative

properties play an important role in thermal

analysis of enclosures with radiatively interacting

surfaces [6]. In such an analysis, the view factor

Fig. 1. Elevation view of various PFCs inside the VV of SST

tokamak.

Fig. 2. The schematic of the cross-sectional view of a PFC

module.

P. Chaudhuri et al. / Fusion Engineering and Design 65 (2003) 119�/132120

plays a key role, which indicates the proportion ofradiation leaving a surface and reaches some other

specified surface by direct radiation transport.

Often the major difficulties in calculating the

radiation exchange rests with the accurate deter-

mination of the view factors [7]. The calculation of

view factors between a particular PFC to the VV

(according to their respective lines of sight) is

difficult as their views are obstructed either bythemselves or by other surfaces in the enclosure.

Here, as the geometry of the PFC along with the

VV is complicated (D shaped VV with number of

PFCs inside as shown in Fig. 1), it is difficult to

calculate the radiated heat loads analytically

between PFC and VV. It is, therefore, necessary

to do these calculations using more than one

method. So, before attempting to solve the fullmodel, a simplified model of concentric cylinders

has been considered whose analytical solution

exists. As it is difficult to do a full fledged 3-D

problem, a 2-D representation of full model has

been considered with the equivalent surface areas

where VV is assumed to be having no ports and is

surrounded by a LN2 (at 80 K) shield. For full

model analysis, the appropriate view factors fordifferent PFC have been calculated by Hottel’s

‘Cross-String’ method [8] and these analytical

results have been compared with the 2-D FE

solutions and found in good agreement for tem-

perature calculated for the two varied by only less

than 10%.

3. Simplified model of concentric cylinders

In the toroidal geometry, the calculation of view

factors of a particular PFC to the VV (according

to their respective line of sight) is not easy to

calculate analytically as their views are obstructed

either by themselves or by other surfaces in the

enclosure. For simplification, and to carry out the

problem, a model of concentric cylinders has beenconsidered whose parametric equations are avail-

able in all standard text books [6,7]. This simpli-

fied model is useful to get an idea of thermal

response of PFC and VV, and their power

requirements during bakeout phases. The simpli-

fied model of concentric cylinders as shown in

Fig. 3, consists of inner, middle and outer cylinder,which represents the PFC, VV and LN2 shield,

respectively. For 2-D FE analysis, these areas are

taken by considering unit length and appropriate

radius of these cylinders. The limitation of this

model is that, here, it is considered that whatever

radiation is coming from VV is entirely received by

all PFC or vice versa. But actually it is not so, the

radiation received by different PFC will be differ-ent according to their line of sight between PFC

and VV inner surface. So, this limitation forces us

to do the radiation calculation on the actual

geometry with appropriate view factor considera-

tions which is described in detail in Section 4.

3.1. Thermal responses of VV and PFC during VV

baking

During the initial phase of operation of SST-1, it

is planned to bake the VV at 250 8C by flowing

hot nitrogen gas through the channels welded on

its inner wall. VV will be baked at constant rate of

heating (10 or 20 8C/h) and all PFC will be baked

by radiation from the heated VV wall, while LN2

shield will be maintained at 80 K through out the

bakeout phase. In the simplified model, the outersurface of the inner cylinder representing as copper

surfaces of PFC, facing the VV wall receives the

radiation, and whole PFC (comprises of copper,

graphite, and a thin layer of flexible graphite) will

get heated up by conduction from that copper

surfaces. The conduction losses from VV to PFC

through the support structures are neglected as it is

found very less compared with radiation losses.Thermal responses of VV and PFC during VV

baking can be written as:

dTVV

dt�Constant for TVVB250 �C

dTVV

dt�0 for TVV]250 �C (1)

(MCuCPCu�MGrCPGr

)dTPFC

dt�Q(VV�PFC) (2)

all symbols are described in Appendix A.

Where, Q(VV�PFC) is the radiation heat transfer

from VV to PFC can be written as:

P. Chaudhuri et al. / Fusion Engineering and Design 65 (2003) 119�/132 121

Three terms in the denominator of Eq. (3)

represent the material resistance due to VV, space

resistance between VV and PFC, and the resis-

tance due to PFC. Similarly the radiation heat

transfer from VV to LN2 shield can be expressed

as:

In the cylindrical model, the radiation emitted

by inner surface of a cylinder (which is concave

shaped) will be received by some portion of its own

surface as they are visible to the radiation coming

from other portions of the surface as shown in Fig.

4A. Where as, the radiation emitted by the outer

surface of a cylinder (which is convex shaped) will

not be received by its own surface as there will be

no direct line of sight between the radiation and its

own surface (shown in Fig. 4B). The same logic or

approximation has been applied here, where PFC,

VV and LN2 shield are represented as three

concentric cylinders as shown in Fig. 3. During

VV baking, the radiation emitted form VV (outer

surface of the middle cylinder in Fig. 3) will be

fully received by the LN2 shield only, so, the view

factor between VV and LN2 shield will be one

(FVV�LN2�/1). On the other hand, since the

radiation emitted by the VV inner surface will

not only be received by the PFCs only, but its own

surface also, so, the view factor will not be one

(FVV�PFC"/1). But, it can be obtained from the

reciprocity relation of view factor (A1F1�/A2F2)

[6,7].

AVVFVV�PFC�APFCFPFC�VV (5)

Since, the outer surface of the innermost cylin-

der (represents as PFC) can not see its own surface

(as it is convex shaped), so the view factor fromPFC (outer surface of inner cylinder) to the VV

wall (inner surface of the middle cylinder) will be

one (FPFC�VV�/1). Accordingly, the middle term

in the denominator of Eq. (3) will be modified as,

A FORTRAN code has been developed to solve

the coupled differential equations Eqs. (1) and (2)

by using the differential equation solver (NAG

library). It calculates the time needed to reach

250 8C for VV and PFC. The temperature time

history of PFC for VV heating rate of 20 8C/h is

shown in Fig. 5 which shows that VV reaches

250 8C at 11.15 h and at that time PFC will reach

102 8C only. PFC will be reaching to 242 8C at 30

h. If it is found that, for 20 8C of VV heating rate,

Q(VV�PFC)�s(T4

VV � T4PFC)

(1 � oVV=oVVAVV) � (1=AVVFVV�PFC) � (1 � oCu=oCuAPFC)(3)

Q(VV�LN2)�s(T4

VV � T4LN2

)

(1 � oVV=oVVAVV) � (1=AVVFVV�LN2) � (1 � oLN2

=oLN2ALN2

)(4)

Q(VV�PFC)�s(T4

VV � T4PFC)

(1 � oVV=oVVAVV) � (1=APFC) � (1 � oCu=oCuAPFC)(6)


the time taken by PFC is unduly long, then, the

rate of heating may be increased in such a way that

required power should not exceed the design

power requirement. Fig. 5 also shows the compar-

ison of analytical results with 2-D FE analysis

using ANSYS and found in very good agreement

with the peak temperature calculated for the two

varied less than 1%. The comparison of this result

is tabulated in Table 1.

The total power requirement for VV during its

baking phase:

QVV(Tot)�MVVCPVV

dTVV

dt�Q(VV�PFC)

�Q(VV�LN2) (7)

The first term in the above equation is respon-

sible for heating the VV upto 250 8C. The second

and third terms represent the radiation losses fromVV to PFC (Eq. (3)) and VV to LN2 shield (Eq.

(4)), respectively. After reaching the baking tem-

perature of 250 8C there will be no more tem-

perature rise of VV, so the first term in the right

Fig. 3. Representations of PFC, VV and LN2 shield for concentric cylinder model.

Fig. 4. Line of sight between two concentric cylinder ex-

changing radiation (A) from outer to inner cylinder, (B) from

inner to outer cylinder.

Fig. 5. Temperature�/time histories of VV and PFC during VV

baking.


hand side of the above equation (Eq. (7)) becomes

zero (as the rate of heating dTVV/dt�/0) and when

PFC reaches 250 8C, the second term becomes

zero (as both are at same temperature, and there

will be no radiation losses between them). So in

steady-state when both VV and PFC reach

250 8C, the power requirement for VV will be

only the radiation loss form VV to LN2 shield(32.85 kW) which is expressed in Eq. (4). The

power requirements for VV (for heating rate of

20 8C/h) is plotted in Fig. 6 which shows that

peak and steady-state power requirement for VV

are 55 and 33 kW, respectively. At lower heating

rate (say 10 8C/h), it is found that the peak power

requirement reduced down to 47.03 kW. If the

design power is less than these values, then, the

rate of heating has to be adjusted accordingly

instead of keeping the rate of heating constant

during ramp up phase.

3.2. Thermal responses of PFC and VV during PFC

baking

During later phases of operation, if graphite

surfaces of the PFC need high temperature baking

(more than 250 8C), then the PFC will be baked at

350 8C independently [4]. The VV need not to be

baked separately, and will be baked by radiation

received from the PFCs. Similar to the VV baking,

Table 1

Thermal responses of PFC during VV baking

Time (h) VV temperature (8C) (heating rate 20 8C/h) PFC temperature (8C)

Analytical (A ) ANSYS (B ) Difference (A�/B )

0 27.00 (room temperature) 27.00 27.00 0.00

5.00 127.00 37.90 37.89 0.01

10.00 227.00 83.74 83.58 0.16

11.15 250.00 101.52 101.30 0.22

15.15 250.00 159.62 159.19 0.43

20.15 250.00 206.20 205.79 0.41

25.15 250.00 230.32 230.06 0.26

30.15 250.00 241.51 241.37 0.14

35.15 250.00 246.40 246.33 0.07

40.15 250.00 248.49 248.45 0.04

Fig. 6. Power requirements of VV during its baking phase. Fig. 7. Temperature�/time histories of PFC and VV during

PFC baking.


the complete heat balance equations for the PFC

baking are:

dTPFC

dt�Constant for TPFCB350 �C

dTPFC

dt�0 for TPFC]350 �C (8)

(MVVCPVV)

dTVV

dt�Q(PFC�VV)�Q(VV�LN2) (9)

where Q(VV�LN2) is defined in Eq. (4) and the

radiation losses from PFC to VV (Q(PFC�VV)) isdefined as,

Fig. 7 shows the results obtained from analytical

and ANSYS solution for thermal response of PFC

and VV during PFC baking. When PFC reaches to

350 8C at 16.15 and 32.30 h for heating rate of 20

and 10 8C/h the VV will reach only at 155 and

182 8C, respectively. This figure also shows that,

during PFC baking VV can attain maximum of

201 8C irrespective of the heating rate of PFC.

This implies that, at this temperature of VV

(201 8C) and PFC (350 8C), the radiation loss

from PFC to VV and from VV to LN2 shield are

equal which is 22.24 kW. Results obtained from

ANSYS are also plotted in this figure which shows

very good agreement with the analytical results.

The discrepancies between them are less than 1%

as tabulated in Table 2. Power requirements of

PFC during baking for heating rate of 20 8C/h is

plotted in Fig. 8, which shows that the peak and

steady-state power requirement for PFC is 41 kW.

For 10 8C/h heating rate of PFC, the power

requirement will be only 32 kW.

3.3. Finite element analysis for simplified model

For a large aspect ratio device, a two dimen-

sional analysis with cylindrical view factors should

be sufficiently accurate [9]. FE analysis for simpli-

fied model of concentric cylinders has been done

on ANSYS [10], where three cylinders are consid-

ered as LN2 shield, VV and PFC, respectively. For

2-D FE analysis, these areas are taken by con-

Table 2

Thermal responses of VV during PFC baking

Time (h) PFC temperature (8C) (heating rate 20 8C/h) VV temperature (8C)

Analytical (A ) ANSYS (B ) Difference (A�/B )

0 27.00 (Room temperature) 27.00 27.00 0.00

5.00 127.00 27.09 27.18 �/0.09

10.00 227.00 55.01 55.02 �/0.01

15.00 327.00 132.05 133.05 �/1.00

16.15 350.00 154.37 155.48 �/1.11

20.15 350.00 193.97 193.64 0.33

25.15 350.00 200.76 200.99 �/0.23

30.15 350.00 201.38 201.57 �/0.19

35.15 350.00 201.44 201.61 �/0.17

40.15 350.00 201.44 201.61 �/0.17

Q(PFC�VV)�s(T4

PFC � T4VV)

(1 � oCu=oCuAPFC) � (1=APFC) � (1 � oVV=oVVAVV)(10)


sidering unit length and appropriate radius of

these cylinders. Fig. 9 shows the 2-D FE repre-

sentation of the simplified model, which is shown

in Fig. 2. The detailed FE model description and

analysis description is given in Section 4.2. The

results of thermal responses of PFC and VV

obtained from ANSYS and analytical calculations

are tabulated in Tables 1 and 2, they are also

shown in Figs. 5 and 7. These figures show that the

analytical and the ANSYS results are in very good

agreement with the peak temperature calculated

for the two varied by less than 1% only.

4. Full model analysis

In full model analysis, the radiation heat loads

from VV to PFC has been calculated during VV

baking only. The calculation of view factor

between VV and PFC is essential to estimate the

radiation transfer between VV and various PFC

like, IDP, IPS, ODP, OPS, and Baffle. The view

factor between two surfaces is defined as the

fraction of energy leaving surface A1 and inter-

cepted by surface A2. Usage of inaccurate view

factor may give very high requirement of radiated

power. It is important to point out that surface

emissivity too plays a critical role in this kind

(radiative heat transfer) of calculation, and the

results are being quite sensitive to this parameter

[11]. Nonetheless, it is very difficult to correctly

estimate a good value for emissivity, since it

greatly depends on the surface polishing and

treatment. From Fig. 10, the view factors between

two surfaces exchanging radiation can be ex-

Fig. 10. Geometric relationship between two surface elements

exchanging radiation.

Table 3

View factors of various PFCs

Different PFC FVV �Cu FVV �Gr

IDP 0.16 0.03

IPS 0.10 0.03

ODP 0.08 0.02. 0.20a

OPS 0.15 0.19, 0.02a

Baffle 0.29 0.24, 0.09a

a Two values of view factors for OPS, ODP and Baffle are

because they are visible to both in-board and out-board side of

the VV wall as shown in Fig. 11.

Fig. 8. Power requirements of PFC during its baking phase.

Fig. 9. 2-D FE representations of concentric cylinders model.


pressed as:

F1�2�1

A1gA1

gA2

cos u1 cos u2

pL2dA1 dA2 (11)

where, A , surface area (m2); L , distance between

dA1 and dA2 (m); u1, angle between normal to dA1

and connecting line between dA1 and dA2; u2,

angle between normal to dA2 and connecting line

between dA1 and dA2.

Calculation of view factors for regular or simplegeometries in radiation heat transfer are well

documented in standard texts [11,12]. Typically,

various analytical methods and contour integral

techniques are used to calculate the view factors

[13] for different geometries. For extremely irre-

gular geometries, however, these methods are not

well suited, but the FEs are quite versatile in this

respect [14]. As the required integration over the

involved finite areas are rather complicated for

this odd geometry, the view factors for different

PFC estimated by Hottel’s ‘Cross String’ method

[7]. The values of view factors for all PFC aretabulated in Table 3. Radiation received by copper

and graphite surfaces of all PFC depends on their

respective line of sight to the VV wall. The line of

sight between VV wall and copper and graphite

surfaces of different PFC are shown in Fig. 11.

4.1. Thermal responses of different PFC

In this full model analysis, the time needed to

reach the baking temperature for a particular PFC

(say IDP) has been calculated independently by

using the following equations.

(MCuCPCu�MGrCPGr

)dTPFC

dt

�Q(VV�Cu)�Q(VV�Gr) (12)

The above equation is same as the Eq. (2),

except the right hand side where QVV�PFC of Eq.

(2) is same as the sum of QVV�Cu and QVV�Gr of

Eq. (12). MCu and MGr are the mass of copper and

graphite, respectively for a particular PFC (say

Fig. 11. Line of sight between various PFC and VV wall.

Fig. 12. Temperature�/time history of all PFC during VV

baking (results obtained from analytical solution of full model

analysis).


IDP) and the value of view factors (from Table 3)

are also employed in the right hand side terms of

this equation, which are expressed as:

According to different view factors for different

PFC and their different surface areas, the radia-tion received by different PFC will be different.

This leads to temperature rise for different PFC

are slightly different (as shown in Fig. 12).

Analytical results of temperature-time profile for

different PFC for VV heating rate of 10 and

20 8C/h are shown in Fig. 12a and b, respectively.

These figures show that when VV is heated slowly

(10 8C/h of VV heating rate) the temperaturedifference between different PFC during ramp up

phase is less than the higher rate of heating

(20 8C/h), which is more preferable for avoiding

the thermal stress between various PFCs.

4.2. Finite element analysis for full model

A full fledged 3-D analysis for the estimation of

baking power requirement will need very high

computer memory, so, a 2-D FE representation offull model has been considered with the equivalent

surface areas where VV is assumed to be having no

ports and is surrounded by a liquid nitrogen (LN2)

shield. The 2-D representations of this model

includes various PFC’s inside the VV is shown in

Fig. 13.

4.2.1. FE model description

The model is discretised with 877 2-D PLANE-

55 elements, 422 LINK-32 elements and 1139

nodes. LINK-32 element is used as the radiationelement on the radiating surfaces for the radiation

heat transfer. Radiative elements were overlaid on

the surfaces of PFC and VV inner surface. The

ANSYS radiation LINK is uniaxial element, which

defines the radiation heat flow rate between PFC

and VV, which are usually the edge of the 2-D

model as shown in Fig. 11. It calculates the view

factors from each element of the PFC to all other

elements (which has direct line of sight) and hence

determines the radiated power loss between VV

and PFC. The aim is to determine the temperature

ramp up in the VV and PFC and the total radiated

power requirements during their bakeout phase.

4.3. FE analysis description

In the FE model the radiation is included

through the use of the AUX12 radiation matrix

generator method. The radiation matrix [15] is

calculated on the basis of the Stefan�/Boltzmann

law of radiation (Eqs. (3) and (4)). The method

described in Ref. [15] involves three main steps:

defining the radiating surfaces, generating the

radiation matrix, using the radiation matrix in

the thermal analysis. The radiating surfaces are

defined on the basis of the existing surface nodes

where appropriate ESURF and SHELL-57 ele-

ments with temperature as a single degree of

freedom. A space node is required to absorb the

radiated energy. The processor AUX12 then

calculates a thermal radiation matrix, which re-

presents radiation effects and view factors between

all surfaces. There is a distinction between the

hidden and the non-hidden method. This matrix is

subsequently declared and used as a superelement

MATRIX50 in the thermal analysis. SHELL-57

are not needed further and deleted before proceed-

ing with thermal analysis.

In ANSYS, the view factors from each element of

different PFC to all other elements (which has

direct line of sight) are calculated by hidden-line

algorithm where it first determines which elements

are ‘visible’ to every other elements [10,15], and,

then calculates the view factors as follows:

Q(VV�Cu)�s(T4

VV � T4Cu)

(1 � oVV=oVVAVV) � (1=AVVFVV�Cu) � (1 � oCu=oCuACu)(13)

Q(VV�Gr)�s(T4

VV � T4Gr)

(1 � oVV=oVVAVV) � (1=AVVFVV�Gr) � (1 � oGr=oGrAGr)(14)


. Each radiating or ‘viewing’ element is enclosed

with a unit hemisphere (semi-circle in 2-D).

. All target or ‘receiving’ elements are projected

onto the hemisphere (or semicircle).

To calculate the view factor, a predetermined

number of rays are projected from the viewing

element to the hemisphere or semicircle. Thus the

view factor is the ratio of the number of rays

incident on the projected hemispherical surface

to the total number of rays emitted by the

viewing elements. In general, accuracy of the

view factor increases with the number of rays,

and the finer mesh spacing of the radiating surface

elements.

Transient and steady-state calculation has been

done in ANSYS by using Frontal Solver with 1.0�/

10�5 accuracy. Initial temperature of whole model

is set at 27 8C (room temperature). Time varying

load (as temperature) is applied on VV surface

upto 250 8C during VV baking, and, upto 350 8Con PFC surface during PFC baking. Constant

material properties (density, specific heat, thermal

conductivities and emissivities) are used for all

materials except the thermal conductivity of gra-

phite, which is considered as a function of

temperature.

5. Results and discussion

Before attempting to do the 2-D FE solution in

ANSYS for the simplified cylindrical model, a

benchmark problem of three concentric cylinders

has been solved in ANSYS and compared with theanalytical solutions. In order to prove the validity

of the code (analytical results), a benchmark

problem of two concentric cylinders has been

solved and compared the result obtained from

ANSYS. The analytical and ANSYS results for

simplified model are in very good agreement as

shown in Figs. 5 and 7. The comparison of these

results are also tabulated in Tables 1 and 2. DuringPFC baking at 350 8C, the VV reaches the steady-

state temperatures of 201.45 8C, which is the

maximum temperature that VV can attain irre-

spective of the heating rate of PFC (Fig. 7). At this

stage the radiation received by VV is same as the

radiation losses from VV to the LN2 shield which

Fig. 14. Comparison of ANSYS and analytical results of thermal

response of PFC and VV (from full model analysis).

Fig. 13. The 2-D-FE model for radiation exchange between

PFC and VV.


is 22.24 kW as shown in Fig. 8. So, there will be no

additional heating or cooling required to keep the

VV at 200 8C. In simplified model analysis it

found that peak power requirement will be less at

lower rate of heating, but it takes more time to the

baking temperature (Figs. 5 and 7). For a given

ramping rate, if the baking time is found unduly

long, then the ramping rate should be increased

according to the designed power. The desired

temperature ramp also depends on the permissible

temperature gradient i.e. thermal stress on VV,

PFC and their connected structures.

From full model analysis, the analytical result

shows that the thermal response of different PFC

are not exactly same, whereas the FE calculation

(ANSYS) shows almost same temperature rise rate

for all PFC as shown in Fig. 14. The comparison

of ANSYS and analytical results obtained from full

model analysis are tabulated in Table 4. The

variation of results are less than 9/10%. From

this we can infer that the calculated values of view

factors (Table 3) give the temperature distribution

of all PFC within 9/10% accuracy. It has also been

seen that the temperature at different depth of the

Table 4

Thermal responses of all PFC for full model analysis

IDP (8C) ODP (8C) IPS (8C) OPS (8C) Baffle (8C)

After 11:15 h

Analytical (A ) 152.1 165.8 167.1 146.4 150.1

ANSYS (B ) 156.1 161.1 160.5 156.1 152.4

Difference (A�/B ) �/4.0 4.7 6.6 �/10.3 �/2.3

After 20:15 h

Analytical 241.9 247.1 248.6 237.6 243.3

ANSYS 244.9 245.2 245.1 244.6 244.7

Difference �/3.0 1.9 3.5 �/7.0 �/1.4

After 30:15 h

Analytical 249.7 249.9 249.9 249.2 249.8

ANSYS 249.9 249.9 249.9 249.8 249.9

Difference �/0.2 0.0 0.0 �/0.6 �/0.1

VV is being heated at constant rate of 20 8C/h, and reaches 250 8C at 11:15 h.

Fig. 15. Temperature of copper, grafoil, and graphite in a PFC

module.Fig. 16. Temperature�/time history of different PFC (result

obtained from simplified and full model of ANSYS analysis).


module (i.e. at graphite surface, copper surfaceand copper�/graphite junction) are almost same

during the entire bakeout phase which means

that there is almost no temperature gradient

exist between the materials in the PFC module

(Fig. 15).

The results of temperature�/time histories ob-

tained by analysing the full model and simplified

model are plotted in Fig. 16. It shows that, thetemperature of all the PFC rises more rapidly in

the case of full model analysis compared with the

simplified model case (cylindrical model). This is

because, in full model analysis, it is considered that

all individual PFC receive radiation by their

copper and graphite surfaces (Eqs. (13) and (14)),

where as in simplified model, it is considered

that all PFC receives radiation by coppersurfaces only (Eq. (3)) and the graphite surfaces

in PFC get heated up by conduction from copper

surfaces. The contribution of higher emissivity for

graphite causes the faster temperature responses

which causes the PFC temperature rise more

rapidly.

6. Summary and conclusions

The thermal response of VV and PFC and their

radiation losses during baking phase have been

evaluated in detail. The calculation of

temperature�/time histories for VV and all PFC

has been also done by FE analysis code (ANSYS).

The time taken by VV and PFC to reach their

respective baking temperatures have to be deter-mined by their rate of heating. If the design power

is less, then, the rate of heating has to be adjusted

accordingly instead of keeping the rate of heating

constant during ramp up phase. In general, the

design must lead to achieve the desired baking

time (ramping time) with small temperature gra-

dients across the material to avoid the excessive

cyclic stresses.Engineering design of most of the sub-systems

of SST-1 have been completed. Fabrication and

assembly contract for the magnets, PFC, vacuum

systems and the support structure has been

awarded. Major materials required for the fabrica-

tion of PFC have been procured and we hope most

of the PFC fabrication will be completed in a fewmonths time. The integration of SST-1 and the

commissioning of PFC inside the vessel are

expected to commence soon. The assembly of

main subsystems of SST-1; supports coils, VV

and cryostat is about to commence shortly. PFC

will be assembled after completion of the VV

assembly and testings.

Acknowledgements

The authors wish to thank H.A. Pathak and E.Rajendra Kumar of vacuum group of SST-1 for

their keen interest in this work.

Appendix A: Nomenclature

AVV surface area of VV (m2)

APFC surface area Cu, facing to the VV inner

surface (m2)

ALN2

surface area of LN2 shield (m2)

CPVV

specific heat of VV (made of SS) (J/kg

K)CP

cuspecific heat of copper (J/kg K)

FVV�PFC view factor from VV to PFC, which is

defined as the fraction of energy

leaving VV inner surface and inter-

cepted by the PFC surfaces

FVV�LN2

view factor from VV to LN2 shield

MVV mass of VV (kg)

MCu mass of copper (includes all PFC) (kg)MGr mass of graphite (includes all PFC)

(kg)

Q(VV�PFC) radiation loss from VV to PFC (W)

Q(PFC�VV) radiation losses from PFC to VV and

VV (W)

Q(VV�LN2) radiation losses from VV to LN2 shield

(W)

TVV temperature of VV (K)TPFC temperature of PFC (K)

Greek symbols

s Stefan�/Boltzmann constant�/5.67�/

10�8 W/m�2 per K�4

oVV emissivity of VV (made of SS)�/0.2


oLN2

emissivity of LN2 shield (made ofSS)�/0.2

oCu emissivity of copper�/0.3

oGr emissivity of graphite�/0.9

Subscripts

Cu copper

Gr graphite

LN2 liquid nitrogen shieldPFC plasma facing components

Tot total

VV vacuum vessel

IDP inner divertor plate

IPS inner passive stabiliser

ODP outer divertor plate

OPS outer passive stabiliser

I-LIM inner limiterO-LIM outer limiter

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study of radiation heat transfer between pfc and vacuum vessel during sst-1 baking

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