5 th Electrohydrodynamics International Workshop Poitiers, France August 30-31, 2004

1. 5th Electrohydrodynamics International Workshop Poitiers, France August 30-31, 2004 HEAT TRANSFER ENHANCEMENT ON THE UPPER SURFACE OF A HORIZONTAL HEATED PLATE IN A POOL BY ION INJECTION FROM A METALLIC POINT Walter Grassi -Daniele Testi -Davide Della Vista LOTHAR (LOw gravity and THermal Advanced Research) laboratory Department of Energetics “L. Poggi” - University of Pisa

2. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 2/17 Aim This work is part of a broader research activity, funded by ESA and aimed at improving the efficiency of thermal control on spacecrafts, by means of the interaction of the electric field with heat transfer. In order to investigate the heat transfer effects of ion injection in point-plane geometry, a versatile experimental apparatus was built, which allowed us to easily mount and substitute the point-electrode and vary its distance from a heated plate.

3. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 3/17 Experimental apparatus (1/2) Scheme of the high voltage electrical circuit vessel dimensions: 200 x 170 x (height) 130 mm3 plate dimensions: 113 x 109 x (thickness) 5 mm3

4. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 4/17 Experimental apparatus (2/2) Seven thermocouples were stuck on the lower side of the plate, which was uniformly heated by two electrical resistance heaters. Two more thermocouples were placed inside the pool at about mid-height, in order to determine the bulk temperature of the fluid. The heat transfer performance was evaluated by means of the Nusselt number (the physical properties were calculated at film temperature): thermocouples’ position under the plate along the x-axis (x=0 at the jet stagnation point)

5. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 5/17 Choice of the dielectric liquid We looked for a space-qualified fluid with goodthermo-hydraulic properties and a low freezing point. Besides, we needed a high electrical resistivity, in order to minimize Joule losses. we chose: perfluorohexane (FC-72 by 3MTM)

6. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 6/17 Point-electrodes Distance from the plate: from 4 to 42 mm • Metals tested: • brass (negative polarity) • steel with 0.4% carbon (negative polarity) • 60%-tin and 40%-lead alloy (positive polarity) • tin-coated copper (positive polarity) Applied high voltage (the heated plate is grounded): 24, 27 and 30 kV brass and steel: cylinder of diameter 3 mm, ending with a cone, sharpened by a grindstone Sn/Pb and Cu/Sn: 0.8 and 0.6 mm wires, sharply cut at an angle of 45° irregular burrs observed under the microscope

7. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 7/17 Discussion of the experimental results (1/6) In natural convection (heat flux: 0.31 W/cm2), prior to the application of the electric field, we measured: Nuexp = 118.6 which is shortly underestimated by the widely used correlation: Nucorr = 0.15*RaL0.33[Bejan, 1993] L = plate area / perimeter Pr > 0.5 107 < RaL < 109 returning: Nucorr = 112.3 (5.6% error)

8. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 8/17 Discussion of the experimental results (2/6) With the brass point we obtained a maximum heat transfer enhancement of 236%. At d = 4 mm, the brass electrode emitted a maximum of 0.27 A, thus dissipating only 8.1 mW inside the liquid. Even at a 30 mm distance from the stagnation point, Nu augmented more than 100% for all the metals. The maxima observable for each Nu distribution are in agreement with the thermal fluid dynamics of impinging jets. Nu vs. x/L distribution, selected, for each point, at the point-to-plate distance (d) giving the highest <Nu>

9. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 9/17 Transfer coefficients distributions for axisymmetric impinging jets In the stagnation region, the vertical velocity is decelerated and transformed into an accelerated horizontal component. Due to the finite breadth of the jet and the exchange of momentum with the quiescent surrounding, the region of accelerated flow ends. The corresponding disappearance of a favorable pressure gradient leads to a sudden rise in turbulence level, resulting in an increase of the transfer coefficients. [Martin, 1977]

10. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 10/17 Discussion of the experimental results (3/6) At low point-to-plate distances (d < 13.5 mm), Nu was nearly constant. At higher d, Nu decreased. Again, this behavior is coherent with the heat transfer characteristics of impinging jets. Nu at the jet stagnation point vs. d/L for the Cu/Sn point

11. Variation of the stagnation Nu with nozzle-to-plate spacing for submerged axisymmetric jets For low nozzle-to-plate spacing, the vertical jet velocity is not affected by mixing and remains nearly constant at the value of the exit velocity. Consequently, in this range, Nu is slightly influenced by the spacing. At higher distances, the impinging velocity declines and heat transfer impairs. [Webb & Ma, 1995] 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 11/17

12. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 12/17 Definition of the EHD-jet Reynolds number The analogy between submerged impinging jets and EHD-induced ones can be extended even farther, defining a Reynolds numberassociated with the ion injection phenomenon: Reinj = u*/ The induced jet velocity can be roughly estimated, assuming a conversion of electric energy into kinetic energy: [Felici, 1969] The diameter of the jet core can be assessed, taking into account Poisson’s equation and free charge continuity: [Atten et al., 1997] Thus: (Iinj is measured by a picoammeter)

13. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 13/17 Discussion of the experimental results (4/6) The simplest correlation for evaluating Nu on the stagnation point of submerged impinging jets is: Nu = C*Re0.5*Pr0.4 with C depending on jet turbulence intensity and mean radial velocity gradient. Interpreting Re as Reinj: C = 1.75(best fit of the data) All the 85 experimental points stayed within the 10% error band, with 68% of them in the 5% band. Relative error of the correlation

14. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 14/17 Discussion of the experimental results (5/6) A more complex correlation, taking into account the effect of the point-to-plane distance, was proposed: Nu = C*Rem*Pr0.4*(d/L)n C = 1.51 m = 0.51 n = -0.058 Again, all the points stayed within the 10% error band, with 82% of them in the 5% band. Relative error of the correlation

15. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 15/17 Effect of an upper confinement for the jet The consequence of the confinement should be the heat transfer impairment, due to the inhibition of the fluid entrainment on the upper side. The tests were conducted with the steel point, at HV = -30 kV. The point-to-plane spacing varied from 4 to 14.5 mm.

16. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 16/17 Discussion of the experimental results (6/6) Nu on the stagnation point ranged from about 80% to about 90% of the corresponding non-confined values, with a lowerworsening at an increased distance. Nu at the jet stagnation point vs. d/L for the steel point

17. 5th Electrohydrodynamics International Workshop Walter Grassi - Daniele Testi - Davide Della Vista University of Pisa 17/17 Concluding remarks • The EHD technique of ion injection yields high heat transfer enhancement, even at a considerable distance from the stagnation point, with negligible power consumption. • An analogy with the thermal fluid dynamics of impinging submerged jets was drawn, showing remarkable similarities both in the Nu distribution along the plate and in the Nu vs. d curve. Particularly, a Reynolds number associated with the ion injection phenomenon was defined. • Two proposed correlations for the Nusselt number showed strong agreement with the experimental data. • Heat transfer impairment due to an upper confinement of the jet was observed.

18. 5th Electrohydrodynamics International Workshop Poitiers, France August 30-31, 2004 HEAT TRANSFER ENHANCEMENT ON THE UPPER SURFACE OF A HORIZONTAL HEATED PLATE IN A POOL BY ION INJECTION FROM A METALLIC POINT Walter Grassi - Daniele Testi - Davide Della Vista LOTHAR (LOw gravity and THermal Advanced Research) laboratory Department of Energetics “L. Poggi” - University of Pisa