5 th electrohydrodynamics international workshop poitiers, france august 30-31, 2004

HEAT TRANSFER ENHANCEMENT ON THE HEAT TRANSFER ENHANCEMENT ON THE UPPER SURFACE OF A HORIZONTAL UPPER SURFACE OF A HORIZONTAL HEATED PLATE IN A POOL BY ION HEATED PLATE IN A POOL BY ION

INJECTION FROM A METALLIC POINTINJECTION FROM A METALLIC POINT

55thth Electrohydrodynamics International Workshop Electrohydrodynamics International Workshop

Poitiers, France Poitiers, France August 30-31, 2004August 30-31, 2004

WalterWalter Grassi Grassi -- DanieleDaniele Testi Testi -- DavideDavide Della Vista Della VistaLOTHARLOTHAR ( (LOLOw gravity and w gravity and THTHermal ermal AAdvanced dvanced RResearch) laboratoryesearch) laboratory

Department of Energetics “L. Poggi” - Department of Energetics “L. Poggi” - University of PisaUniversity of Pisa

This work is part of a broader research activity, funded by This work is part of a broader research activity, funded by

ESAESA and aimed at improving the efficiency of thermal and aimed at improving the efficiency of thermal

control on spacecrafts, by means of the control on spacecrafts, by means of the interactioninteraction of the of the

electric fieldelectric field with with heat transferheat transfer..

In order to investigate the In order to investigate the heat transfer effectsheat transfer effects of of ion ion injectioninjection in in point-planepoint-plane geometry, a versatile geometry, a versatile

experimental apparatus was built, which allowed us to experimental apparatus was built, which allowed us to

easily mounteasily mount and and substitutesubstitute the the point-electrodepoint-electrode and and

varyvary its its distancedistance from a from a heated plateheated plate..

AimAim


Walter Walter GrassiGrassi - Daniele - Daniele Testi Testi - Davide - Davide Della VistaDella Vista University of University of PisaPisa2/172/17

Experimental apparatus Experimental apparatus (1/2)(1/2)

Scheme of the high voltage Scheme of the high voltage electrical circuitelectrical circuit

vessel dimensions: vessel dimensions: 200200 x x 170170 x (height) x (height) 130 mm130 mm33

plate dimensions: plate dimensions: 113113 x x 109109 x (thickness) x (thickness) 5 mm5 mm33



Experimental apparatus Experimental apparatus (2/2)(2/2)

thermocouples’ position under the plate along the thermocouples’ position under the plate along the xx-axis (x=0 at the jet stagnation point)-axis (x=0 at the jet stagnation point)

Seven thermocouplesSeven thermocouples were were stuck on the stuck on the lower sidelower side of the of the plateplate, which was , which was uniformly uniformly

heatedheated by two electrical by two electrical resistance heaters.resistance heaters.

Two more thermocouplesTwo more thermocouples were were placed placed inside the poolinside the pool at about at about

mid-heightmid-height, in order to determine , in order to determine the the bulk temperaturebulk temperature of the of the

fluid.fluid.

The The heat transfer performanceheat transfer performance was evaluated by means of the was evaluated by means of the Nusselt numberNusselt number (the physical (the physical

properties were calculated at film properties were calculated at film temperature):temperature):



Choice of the dielectric Choice of the dielectric liquidliquid

We looked for a We looked for a space-qualifiedspace-qualified fluid with fluid with goodgood thermo-hydraulic thermo-hydraulic propertiesproperties and a and a low freezing pointlow freezing point. Besides, we needed a . Besides, we needed a high high

electrical resistivityelectrical resistivity, in order to , in order to minimize Joule lossesminimize Joule losses..

perfluorohexaneperfluorohexane(FC-72 by 3M(FC-72 by 3MTMTM))

we chose:we chose:



Distance from the plateDistance from the plate::from 4 to 42 mmfrom 4 to 42 mm

Point-electrodesPoint-electrodes

irregular irregular burrs burrs

observed observed under the under the

microscopemicroscope

Metals testedMetals tested::• brass brass (negative polarity)(negative polarity)

• steel with 0.4% carbon steel with 0.4% carbon (negative polarity)(negative polarity)

• 60%-tin and 40%-lead alloy 60%-tin and 40%-lead alloy (positive polarity)(positive polarity)

• tin-coated copper tin-coated copper (positive polarity)(positive polarity)

brass and steel: brass and steel: cylinder of diameter cylinder of diameter 3 mm, ending with a cone, sharpened 3 mm, ending with a cone, sharpened

by a grindstoneby a grindstone

Sn/Pb and Cu/Sn: Sn/Pb and Cu/Sn: 0.8 and 0.6 mm wires, 0.8 and 0.6 mm wires, sharply cut at an angle of 45°sharply cut at an angle of 45°

Applied high voltage Applied high voltage (the heated plate is grounded)(the heated plate is grounded)::

24, 27 and 30 kV24, 27 and 30 kV



Discussion of the experimental results Discussion of the experimental results (1/6)(1/6)

In In natural convectionnatural convection (heat flux: (heat flux: 0.31 W/cm0.31 W/cm22), prior to ), prior to the application of the electric field, we measured:the application of the electric field, we measured:

NuNuexpexp = 118.6 = 118.6

which is shortly underestimated by the widely used which is shortly underestimated by the widely used correlation:correlation:

NuNucorrcorr = 0.15*Ra = 0.15*RaLL0.330.33 [Bejan, 1993][Bejan, 1993]

L = plate area / perimeterL = plate area / perimeter

Pr > 0.5Pr > 0.5

101077 < Ra < RaLL < 10 < 1099

returning:returning:

NuNucorrcorr = 112.3 = 112.3

(5.6% error)(5.6% error)



With the With the brassbrass point we obtained point we obtained a a maximummaximum heat transfer heat transfer enhancementenhancement of of 236%236%..

At d = 4 mm, the brass electrode At d = 4 mm, the brass electrode emitted a emitted a maximummaximum of of 0.27 0.27 AA, , thus thus dissipatingdissipating only only 8.1 mW8.1 mW

inside the liquid.inside the liquid.

Even at a Even at a 30 mm distance30 mm distance from from the stagnation point, Nu the stagnation point, Nu

augmented more than 100% augmented more than 100% for all the metals.for all the metals.

The The maximamaxima observable for each observable for each Nu distribution are in Nu distribution are in agreementagreement with the with the thermal fluid dynamicsthermal fluid dynamics

of of impinging jetsimpinging jets..Nu vs. x/L distribution, selected, for each Nu vs. x/L distribution, selected, for each point, at the point-to-plate distance (d) point, at the point-to-plate distance (d)

giving the highest <Nu>giving the highest <Nu>




Transfer coefficients distributions Transfer coefficients distributions for axisymmetric impinging jetsfor axisymmetric impinging jets

In the In the stagnation stagnation regionregion, the , the verticalvertical

velocity is velocity is decelerateddecelerated and and

transformedtransformed into an into an accelerated accelerated horizontalhorizontal component.component.

Due to the Due to the finite finite breadthbreadth of the jet and of the jet and

the the exchange of exchange of momentummomentum with the with the

quiescent surrounding, quiescent surrounding, the region of the region of

accelerated flow accelerated flow endsends..

[Martin, 1977][Martin, 1977]



The corresponding The corresponding disappearancedisappearance of a of a favorable favorable pressure gradientpressure gradient leads to a leads to a sudden risesudden rise in in

turbulenceturbulence level, resulting in an level, resulting in an increaseincrease of the of the transfer coefficientstransfer coefficients..

At At lowlow point-to-plate point-to-plate distances (d < 13.5 distances (d < 13.5 mm), mm), NuNu was nearly was nearly

constantconstant..

At At higherhigher d, Nu d, Nu decreaseddecreased..

Again, this behavior Again, this behavior is is coherentcoherent with the with the

heat transfer heat transfer characteristicscharacteristics of of impinging jetsimpinging jets..

Nu at the jet stagnation point vs. d/L Nu at the jet stagnation point vs. d/L for the Cu/Sn pointfor the Cu/Sn point




Variation of the stagnation Nu with Variation of the stagnation Nu with nozzle-to-plate spacing for nozzle-to-plate spacing for

submerged axisymmetric jetssubmerged axisymmetric jets

For For low nozzle-to-plate low nozzle-to-plate spacingspacing, the vertical jet , the vertical jet

velocity is not affected by velocity is not affected by mixing and mixing and remains nearly remains nearly constantconstant at the value of the at the value of the exit velocity. Consequently, exit velocity. Consequently, in this range, in this range, NuNu is is slightly slightly influencedinfluenced by the by the spacingspacing..

At At higher distanceshigher distances, the , the impinging velocity impinging velocity declinesdeclines and and heat heat transfer impairstransfer impairs..

[Webb & Ma, 1995][Webb & Ma, 1995]



Definition of the EHD-jet Reynolds numberDefinition of the EHD-jet Reynolds number



The The analogyanalogy between submerged impinging jets and EHD-induced between submerged impinging jets and EHD-induced ones can be extended even farther, ones can be extended even farther, definingdefining a a Reynolds numberReynolds number associated withassociated with the the ion injectionion injection phenomenon: phenomenon:

ReReinjinj = u* = u*//

The induced jet velocity can be roughly estimated, assuming a The induced jet velocity can be roughly estimated, assuming a conversion of electric energy into kinetic energy:conversion of electric energy into kinetic energy:

u Ε u Ε

[Felici, 1969][Felici, 1969]

The The diameterdiameter of the of the jet corejet core can be can be assessedassessed, taking into , taking into account Poisson’s equation and free charge continuity:account Poisson’s equation and free charge continuity:

injΙ du

[Atten et al., 1997][Atten et al., 1997]

Thus:Thus: injinj

Ι dRe

= (I(Iinjinj is measured by a picoammeter) is measured by a picoammeter)

Relative error of the correlationRelative error of the correlation




The simplest The simplest correlationcorrelation for for evaluating Nuevaluating Nu on the stagnation on the stagnation point of submerged impinging jets is:point of submerged impinging jets is:

Nu = C*ReNu = C*Re0.50.5*Pr*Pr0.40.4

with with CC depending on jet turbulence intensity and mean depending on jet turbulence intensity and mean radial velocity gradient.radial velocity gradient.

Interpreting ReInterpreting Re as as ReReinjinj::

C = 1.75C = 1.75 (best fit of the data)(best fit of the data)

All All thethe 85 experimental 85 experimental points points stayedstayed within within the the

10% error band10% error band, with, with 68% 68% of them in theof them in the 5% band 5% band..

C = 1.51C = 1.51m = 0.51m = 0.51

n = -0.058n = -0.058

Again, Again, allall the the pointspoints stayed stayed

within within thethe 10% 10% error banderror band, with , with

82% 82% of them in the of them in the 5% band5% band..




A more complex A more complex correlationcorrelation, taking into account the effect of the , taking into account the effect of the point-to-plane distance, was proposed:point-to-plane distance, was proposed:

Nu = C*ReNu = C*Remm*Pr*Pr0.40.4*(d/L)*(d/L)nn

Relative error of the correlationRelative error of the correlation

Effect of an upper confinement for the jetEffect of an upper confinement for the jet



The The consequenceconsequence of the of the confinementconfinement should be the should be the heat heat transfer impairmenttransfer impairment, due to the , due to the inhibitioninhibition of the of the fluid fluid

entrainment onentrainment on the the upper sideupper side..

The tests were The tests were conducted with conducted with

the the steel pointsteel point, , at at HV = -30 kVHV = -30 kV..

The The point-to-point-to-plane spacingplane spacing varied from varied from 4 4 to to

14.5 mm14.5 mm..




NuNu on the stagnation point on the stagnation point rangedranged from about from about 80%80% to about to about 90%90% of the corresponding of the corresponding non-confinednon-confined values, with a values, with a lowerlower

worseningworsening at an at an increased distanceincreased distance..

Nu at the jet stagnation point vs. d/L Nu at the jet stagnation point vs. d/L for the steel pointfor the steel point

Concluding remarksConcluding remarks

• The EHD technique of The EHD technique of ion injectionion injection yields yields high heat transfer high heat transfer enhancementenhancement, even at a considerable distance from the stagnation , even at a considerable distance from the stagnation

point, withpoint, with negligible power consumption negligible power consumption..

• An An analogyanalogy with the thermal fluid dynamics of with the thermal fluid dynamics of impinging impinging submerged jetssubmerged jets was drawn, showing was drawn, showing remarkable similaritiesremarkable similarities both both

in the in the Nu distribution along the plateNu distribution along the plate and in the and in the Nu vs. d curveNu vs. d curve. .

Particularly, a Particularly, a Reynolds numberReynolds number associated with the associated with the ion injectionion injection

phenomenon was defined.phenomenon was defined.

• Two Two proposed proposed correlationscorrelations for the Nusselt number showed for the Nusselt number showed strong strong agreementagreement with the experimental data. with the experimental data.

• Heat transfer impairmentHeat transfer impairment due to an due to an upper confinementupper confinement of the of the

jet was observed.jet was observed.



HEAT TRANSFER ENHANCEMENT ON THE HEAT TRANSFER ENHANCEMENT ON THE UPPER SURFACE OF A HORIZONTAL UPPER SURFACE OF A HORIZONTAL HEATED PLATE IN A POOL BY ION HEATED PLATE IN A POOL BY ION

INJECTION FROM A METALLIC POINTINJECTION FROM A METALLIC POINT


Poitiers, France Poitiers, France August 30-31, 2004August 30-31, 2004

WalterWalter Grassi Grassi - Daniele- Daniele Testi Testi - Davide- Davide Della Vista Della VistaLOTHARLOTHAR ( (LOLOw gravity and w gravity and THTHermal ermal AAdvanced dvanced RResearch) laboratoryesearch) laboratory

Department of Energetics “L. Poggi” - Department of Energetics “L. Poggi” - University of PisaUniversity of Pisa

5 th electrohydrodynamics international workshop poitiers, france august 30-31, 2004

Documents

plate distance d

heat transfer performance

horizontal heated plate

low freezing point

brass negative polarity

pointplane geometry

brass electrode

xaxis x