ICEC 15 Proceedings

Supercritical helium cooling of a cable in conduit conductor with an inner tube

Andr6 Martinez* Jean-Luc Duchateau* Gilbert Bon Mardion*

Aiain Gauthier** Bernard Rousset**

*Centre d'Etudes de Cadarache Association Euratom-CEA sur la fusion, D~partement de Recherches sur la Fusion Control~e, 13108 Saint Paul Lez Durance, FRANCE

**Centre d'Etudes Nuclraire de Grenoble, Service des Basses Temp&atures, 85X- 38041 Grenoble, FRANCE

In the design of forced flow cooling systems of large superconducting magnets for plasma confinement in future fusion reactor, the time needed, after a heat pulse (caused by magnetic field variations), for the cable to be recooled at the initial fluid temperature is an important design parameter. The conductor proposed for these coils, is cooled by a supercritical helium flow in two parallel channels: a peripherical zone, which contains the cable, with a low helium velocity and a channel with a high velocity (cooling path as long as 1000 m). An experiment has been carried out in a C.E. Grenoble facility with two types of cable in conduit (one with an inner tube, one without an inner tube) to check a thermohydraulic model.

INTRODUCTION

For a cable in conduit without an inner channel, the time needed, after a heat pulse, for the cable to be recooled at the initial fluid temperature is simply given by the length divided by the fluid velocity. However, for a conductor with a central cooling channel (see Fig n°l), the effective circulating time cannot be simply evaluated through the average velocity (i.e. the total helium mass of the conductor divided for the total mass flow rate). An analytical solution of the outlet temperature variation of the fluid for the two channels [1] allowed this

recooling time to be estimated as the sum of two time durations: the average recooling time determined with the average velocity, and a "train effect" depending, in particular, on the heat transfer coefficient between the peripheral zone and the central channel. In the report [1], this analytical solution has been compared with the values given by a numerical model (which takes into account the shape of the heat pulse). The experiment which has been carried out in C.E.Grenoble , allows to compare experimental and computed temperatures at different locations. The aim in particular, is to show that the friction factor in the two parallel channels of the conductor, and the heat transfer coefficient between the helium in the peripheral zone and the helium in the central zone are taken into account appropriately in the code.

MATHEMATICAL MODEL

In the external annulus, the fluid flows with velocity U~ in the direction of the axis x. Let p~ be the density

and Cp~ the specific heat of this fluid, and let T~ be its temperature at point x and at time t. Two cases have been considered : the annulus can be separated or not from the inner channel by a tube. The respective inner fluid characteristics are density P2, specific heat Cp2 , and T 2 is the temperature at point x

and at time t. U: is the velocity in the x direction. Let H be the heat transfer coefficient across the inner tube; the rate of flow of heat across the wall at x is H(T~ -T2) . Taking into account the different thermal barriers for the heat transfer between the two

channels, H is given by the expression :

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1 1 1 ] m = m + +

H P,h, 2~zK P=h~

P1 : external wetted perimeter of the inner tube

P2: internal wetted perimeter of the inner tube

P~: average wetted perimeter of the inner tube

h~ : heat transfer from fluid in annulus to the inner tube K : thermal conductivity o the inner tube h~: heat transfer from fluid in the inner tube to the tube

In terms of partial differential equation, the conservation equation for energy for an unsteady incompressible fluid flow in one dimension (conductive effects being neglected) may be written as follows

for the fluid in the annulus •

c3T~ i_ U 3T~ + ~B,(T _ T~) = Q(t) (1) Ot Ox

and for the fluid in the inner tube

+uOr - 13 _(T, - = 0 a

(2)

where ]~i - H.Pm with i = 1 for the annular flow and i = 2 for the internal flow, Spi is the helium PiCPiSPi ,

cross section. We suppose both fluids to be at the initial temperature T0(x ) (constant heat radiation), before a given heat

power Q( t ) is deposited in the annulus. Q( t ) is constant over the length. The effect of the variations of

the pressure is not taken into account. The fresh fluid (cold fluid) enters in both channels at x = 0. The numerical method used for solving the hyperbolic partial differential equations (1) and (2) is the method of characteristics. This method is described in reference [2].

EXPERIMENTAL SET-UP AND DATA

The conductor proposed for these thermohydraulic experiments exhibits geometrical characteristics similar to those of the conductors imagined for the large superconducting magnets (ITER for instance). An experimental loop comprising 30 m of cable in conduit conductor was developed by C.E.A. to analyse its thermohydraulic behaviour when it is maintained at low temperature by cooling with forced flow pressurized helium. The superconducting strands of this conductor have been replaced by copper wires to allow heat to be easily deposited.

The experimental loop is made of two types of cable in conduit conductor. The respective cross sections of each cable are shown in Figure 1. Each length L of conductor is equal to 15 m.

- the first type is jacketed into a stainless steel tube with an inner diameter of 17 mm. It is made up of copper wires assembled in 6 petals placed in an annular space limited by a second tube with an inner diameter of 4.4 mm.

- in the second type, the internal tube has been removed and the helium flowing in the annular space through the conductor is now directly in contact with the helium flowing in the central channel.

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ICEC 15 Proceedings

This conductor is installed in the premises of the CENG/SBT in a cryogenic test stand described in a previous report [3 ]. The experiment consists in the transient heating by one or more pulses of the conductor, by supplying some electric current. The joule heating is uniform along the length. In order to operate in areas where the thermodynamic properties of supercritical helium are not subjected to excessively abrupt variations, the working pressure is set at 7 bars, the temperature in the loop remaining between 5 and 7 K. For these tests, a centrifugal pump can deliver 5 g/s of helium under 200 mbars.

EXPERIMENTAL RESULTS AND SIMULATIONS

The friction factor L (~, = 2 .Ap .dh /P .U~: .L, d h is the hydraulic diameter and Ap is the pressure droi~) in the external annulus was measured by steady state pressure drop experiments (the inner tube was closed using a valve at the heated extremity x = 0). The influence of the pipe curvature is neglected. It is described in Figure 4. The friction factor in the inner tube is the classical relation given for smooth tubes. Consequently, for the conductor with inner tube, about 1/3 of the total mass flow rate flows in the

external annulus and 2/3 in the inner tube. In the same way, for the conductor without inner tube, only ten per cent of the total mass flow rate flows in the external annulus and ninety per cent in the inner channel. The main advantage of the conductor without the inner tube is to offer a low pressure drop in comparison to the pressure drop of the conductor with inner tube (about three times lower). For the conductor without the inner tube the heat transfer coefficient H = 600 W/mZ:K seems to give the best agreement both in shape and magnitude to the total temperatures measured experimentally. In the same way, for the conductor with the inner tube, the heat transfer coefficient is H = 200 W/m2.K. For these values of the heat transfer coefficient, the difference between the temperature of the annulus and the temperature of the inner channel is low. In Figure 2, the temperature computed in the locations corresponding to the sensors of the conductor without the inner tube is shown. The agreement with the experimental measurements is very good for both sensors at x = 9.6 m and x = 14.3 m, while some mismatch appears for the sensors at x = 4.8 m and x = 7.2 m. This is certainly due to the effect of the boundary conditions (the heat radiation is not constant over the length of the conductor). Figure 3 reports the computed temperatures in the sensors of the conductor with tube, compared to the experimental measurements. Here a clear disagrement is found for the sensors at x=4.8 m and x = 9.6 m for the same reason.

CONCLUSIONS

The numerical method developed here enables to check the thermohydraulic behaviour of a conductor recooled by a supercritical helium flow in two parallel channels. The accuracy of the method is generally good, and satisfactory agreement is found with experimental data. This is certainly within the limits of uncertainties of the experimental set-up and boundary conditions.

REFERENCES

1 MARTINEZ A.and TURCK B., Supercritical helium cooling of a cable in conduit conductor with an inner tube. Paper submitted for publication in CRYOGENICS, March 1994. 2 THORLEY and H.TILEY, Unsteady and transient flow of compressible fluids in pipelines. A review of theoretical and some experimental studies. Heat and Fluid Flow, March 1987. 3 ROUSSET B. and al, Operation of forced flow superfluid helium test facility and first results. International Cryogenic Engeneering Conference 14 (1992) pp 134-137.

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Figure 1: The respective cross sections of the two types of cable in conduit conductor

Flow rate 0 . 9 3 gls,Pulse 2 . 2 5 W - 5 0 s Flow rate 0.66 g/s, Pulses 2.25 W (25s/100s|

6.2 6

~d bd 6 x = 1 4 . 3 m

x = 9 . 6 m

x = 7 . 2 m ~ 5 . 6 o,I

E 5.8 x = , .s in E

I-- x = O . O m I ~

5.6 5.2 0 200 400

Time (s)

~ x = 1 4 . 3 m

~ ~ ~ ~ ~ F ~ x 4 . 8 m

~ x = O . O m

0 200 400 600

Time (s)

Figure 2 : Conductor without inner tube, comparison of computed (thick line) and experimental (fine line) temperature at different sensors locations

Flow rate 0 . 9 3 g/s, Pulse 2 . 2 5 W-50s Flow rate 0.66 g/s, Pulses 2.25 W (25s/100s)

6.5 6.4

x = 1 4 . 3 m

== x = g.em 2

6 2 5 , = , s o 6 1

i i !-- x = O . O m I ' -

6 5.8 0 1 O0 200 300 0 200

Time (s) Time (s)

x = 1 4 . 3 m

x = 9 . 6 m

X = 4 . 8 m

x = O . O m

Figure 3 : conductor with inner tube. comparison of computed (thick line) and experimental (fine line) temperature at different sensors locations

400

~ -~ 0.11

"- c 0.09 e- ¢= o .= ~ 0.07

.=_ 0.05

Figure 4

[3 [3

5000 10000

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1 5 0 0 0