Boiling heat transfer of liquid nitrogen in the presence of electric fields

P Wang, P L Lewin , D J Swaffield and G Chen

University of Southampton, Southampton, UK

Experimental setup and electrode system

Experimental results and discussionIntroduction

Experimental results and discussion

Conclusions

An experimental study has been undertaken to determine the influence of a d.c. uniform electrical field on boiling heat transfer of liquid nitrogen (LN2).

A copper block electrode with temperature measurement and vacuum heat insulation was designed and manufactured.

The effects of electric fields on boiling hysteresis, nucleate boiling and critical heat flux have been analyzed and discussed.

The results obtained may help the design of the LN2 related components for HTS device cooling and also provide an initial perspective on the possible improvements for cryogenic cooling of HTS equipment.

The boiling curves of LN2 have been obtained with and without electric fields. The results show: 1) the electric field is able to reduce the first hysteresis of LN2. i.e. the higher the electric field the easier to active nucleate boiling with a lower heat input. 2) A second hysteresis phenomenon of LN2 exists for increasing heat and decreasing heat flux test conditions. A higher electric field tends to eliminate the hysteresis phenomenon. 3) Electric fields can enhance nucleate boiling heat transfer of LN2. 4) The CHF can be enhanced by the electric field, for this experiment a 14% increase is obtained under an applied 40 kV high voltage. 5) There is no noticeable polarity effect on boiling heat transfer.

Experimental tests were carried out using commercial grade LN2 at atmospheric pressure. The LN2 was renewed after all data for each boiling curve had been obtained.

A mesh-plane electrode configuration was used. The high-voltage electrode is brass mesh (1 mm wire in diameter and 2.36 mm in width mesh). The grounded electrode is a special cylindrical copper block with a heater and a vacuum jacket. The boiling process takes place on the top centre surface of the copper block (Fig.2).

Fig.3 First hysteresis of LN2 under high positive voltages

• Mesh-plane electrodes

• Electrode gap: 10 mm

• Heater power up to 450 W

• +/- 0-40 kV power supply for both polarities

• 3 pt100s for temperature measurement

• Vacuum insulates the copper block from its surroundings

• High-speed camera for observation and recording of images

Effect of electric field on the boiling hysteresis

Fig.1 Schematic diagram of the experiment

Fig.3 shows the effect of the electric field on the first hysteresis of LN2. It can be seen that the magnitude of the first hysteresis reduces with increasing voltage. Thereby decreasing the degree of the superheat required to start nucleate boiling. The reasons for the decrease of the first hysteresis under electrohydrodynamic (EHD) conditions is due to the reduction of the thermal boundary layer caused by an electroconvective movement in the presence of electric fields and then the electrical activation of nucleation sites.

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∆T (K)

Hea

t fl

ux

(W/c

m2)

V= 0kV increasing heat

V= +10kV increasing heat

V= +30kV increasing heat

V= +40kV increasing heat

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∆T (K)

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Fig.2 A photograph of boiling of LN2

Fig.4a shows the second boiling hysteresis phenomenon that exists for increasing heat flux and decreasing heat flux conditions under a zero-field. Fig. 4b and c show the effect of an applied DC positive voltage of 10 and 20 kV on this hysteresis, respectively. It is seen that application of an electric field can decrease the second hysteresis, particularly the hysteresis disappears for high voltages in excess of 20 kV for this electrode arrangement. By analyzing the energy of a bubble formation in an electric field, the effect of the electric forces on the nucleation process shows the overpressure in the vapor phase as a function of the electric field can be expressed as: 2

03 ( )2 2( ( ))

4(2 )l l v

v ll v

EP P r E

r r

where ε0 is the dielectric constant in vacuum, εl is the dielectric permittivity of liquid, εv is the dielectric permittivity of saturated gas in bubble, E is the electric field strength, r is the equivalent radius of the deformed bubble for EHD boiling, the pressure difference Pv-Pl is the sum of capillary pressure, characterized by the fluid surface tension σ, and an electrostatic pressure characterized by an apparent surface tension σ(E), which is proportional to the square of the electric field strength. The electric field modifies the surface tension so that the fluid has non-wetting fluid behaviour. According to this analysis, for LN2, the ratio σ(E)/σ is about 48% and 108% for 20 and 30 kV conditions, respectively. This shows that the pressure of the electric field on the bubble is substantial in comparison with the capillary pressure. The increase of σ(E) with electric field gives a reason for the reduction of the hysteresis phenomenon and result in the activation of nucleation sites being easier under increasing heat flux conditions.

Effect of electric field on nucleate boiling

Effect of electric field on the critical heat flux (CHF)

Fig.7 CHF as a function of the high voltage

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∆T (K)

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t fl

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V= +10kV increasing heat

V= +20kV increasing heat

V= +30kV increasing heat

V= +40kV increasing heat

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Applied voltage (kV)

Cri

tical

hea

t flu

x, q

CH

F (W

/cm

2 ) Negative

Positive

where ρl is the density of liquid and ρv is the density of vapour. For LN2, λd is about 11mm in zero-field conditions. The presence of an electric field can modify the liquid-vapour interface stability. In this case, the wavelength λd taking into account the electric field effects is given by

1/ 2

2 3( )d

l v g

Fig.7 shows the electric field effect on CHF. The CHF obtained in zero-field is about 24.5 W/cm2 and for this experiment a 14% increase can be obtained for an applied voltage of 40 kV. Very similar results have been obtained for positive and negative high voltages. A model of the liquid-vapour interface stability has been given to explain the increase under electric fields. Without electric field conditions, near the CHF, the vapour columns flow adjacent to the liquid along an interface that is unstable under the action of inertia and surface tension forces. A maximum relative vapour rate exists, above which a small disturbance is amplified and causes the distortion of the flow. The wavelength of the disturbance with the largest growth rate is called the most dangerous wavelength, λd. For a plate surface, λd is defined as follows:

2 2 2 1/ 2

6 2

( ( 3 )doG G B

2 22 2,l vo

g EB G

Fig.5 shows the nucleate boiling curves of LN2 obtained under different high-voltages with both increasing and decreasing heat flux. It is seen that the EHD effect can enhance heat transfer, i.e. the heat flux q increases with increasing voltage for a given ∆T. Especially, the EHD enhancement is very obvious for applied voltages over 20 kV. When nucleate boiling appears and with no electric field condition, the heat transfer mechanisms are governed by three factors: heat conduction through the macrolayer surrounding the bubble interface, evaporation of the microlayer located between the heated surface and the bubble bottom, and convection within the LN2 adjacent to the bubble and the heated surface (Fig.6a). For EHD nucleate boiling conditions (Fig.6b), as the appearance of volume electric force,

Fig.4 Second hysteresis phenomenon: (a) 0kV, (b) +10kV, (c) +20kV.

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∆T (K)

Hea

t fl

ux

(W/c

m2)

V= 0kV decreasing heat

V= +10kV decreasing heat

V= +20kV decreasing heat

V= +30kV decreasing heat

V= +40kV decreasing heat

b

where δ is the vapour film thickness that covers the heating surface. The bond number Bo and G, which represents the ratio of the electric forces to the surface tension forces, are given by

For LN2, λd is about 3 mm for an electric field strength of 20 kV/cm. This shows electric fields can decrease the λd and break the vapour film and consequently increase the CHF.

Fig.5 Nucleate boiling curve of LN2 under different positive voltages. (a) increasing heat, (b) decreasing heat

Fig.6 Nucleate boiling heat transfer mechanisms. (a) under zero-field conditions, (b) under EHD conditions

electroconvective movements are induced within the liquid region. Thus, the macrolayer thickness decreases and heat transfer within the macrolayer is increased. The electric force tends to maintain the bubble against the heat transfer surface, causing intense vaporization of the microlayer between the bottom of the bubble and the heating surface. The heat transfer enhancement through both the macrolayer and the microlayer encourages rapid growth of bubbles, increasing their departure volume. More heat energy can be effectively transferred. Thus, effectively causing the electrode surface temperature to decrease.

a b