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Drop carry-over phenomenon in liquid evaporation from capillary structures
LEITERS IN HEAT AND MASS T R A N S F E R 0094-4548/78/1101-0339502.00/0 Vol. 5, pp. 339-347, 1978 © Pergamon Press Ltd. Printed in Great Britain
DROP CARRY-OVER PHEN0~ENON IN LIQUID EVAPORATION PROM CAPILLARY STRUCTURES V.I.Tolublnsky, V.A.Antonenko, Yu.N.0stzovsky, E .N. She vchuk Institute of Engineering Thermophysics,Kiev,USSR
(C~,.~nicated by OoG. Martynenko and R.I. Soloukhin)
ABSTRACT
It has been experimentally established that heat transfer from the surface of the liquid-laden capillary-porous material is accomplished by evaporation from the free surface of menisci and is accompanied by carryover of drops of the womkimg fluid. The reason for this phenomemon is non-unifoxmity of liquid supply towards separate cells of the structure or non-unifommity of thermal conditions at the heating surface. The spraying intensity depemds on the geometrical ohazacteristios of the capillary structure, physical properties of the liquid, and pressure.
Ex~e ,riment,al The paper presents the results of an experimental study of the vapor formation mechanism in capillary structures of heat pipe wicks. The experiments were oond-,oted on the set-up, described in fl~, with the workin~ element in the form of a copper %herm~l wedge which imitated the evaporation region of a heat pipe (Pig. I). The stwuoture investigated was closely attached to a 28 ramdid enf-faoe heating surface of the wedge. The height of liquid in the chamber was kept 1-2 mm below the level of the heating smrfaee, with the contour of the wick being completely immersed in liquid. Thus, Just as in heat pipes, the cooling liquid was supplied to the heating surface by capill~ry forces only. 339
340
V.l. Tolubinsky, et al.
Vol. 5, No. 6
8
i m
FIG. i Schematic diagram of the set-up: I, thermal wedge ; 2, capillary structure. The heat flux density and the heating surface temperature were determined by the temperature gradient along the body of the wedge. The test chamber was provided Wi+~ vlewi~g windows of quartz glass for visual observations, graphic inspe orlon.
cinema- and photo-
The experiments were carried out with distilled water in the pressure range frc~ 0.02 to 0.4 ~ a and with buthyl alcohol, normal h e p ~ i n , acetone and benzole at a~mospheric pressure in capillary structures which are most characteristic of the heat pipe wlcks~ i.e. screensp metal fibres and perforated screens ( 35 types in all ). Direct visu81 observations of the pxocesses occurring on the surface of porous specimens have shown that at h~gh heat flux densities (for e~ample, for water at q > 150-200 kW/m 2) liquid evaporates from the surface of the menisci of capillary pores with no boiling. Even at the pressure of 0.02 KPa and the heat flux density of 700 kW/m 2, vapor bubbles do not form on the surface of the wicks ( t ~ % can allow this heat load, of course). In this case, the curvilinear surfaces of menisci is clearly observed.
Vol. 5, No. 6
LIQUID EVAPORATION FROM CAPr~ZARY ~
341
It has been established in the course of the experiments that evaporation from the free surface of menisci in capillary structures is accompanied by capillary carry-over of liquid. Expulsion of liquid from the wicks of heat pipes was noted long ago [2,3J, but was related to collapse of vapor bubbles in boiling. The experiments have shown that the intensity of drop carry-over depends on pressure and increases with decrease in the latter. Under vacuum, the carry-over is such that often makes visual observations difficult. However, already at 0.~ MPa, the carry-over is practically absent. This, by the way, once more confirms the absence of boiling in pores of capillary structures, since in the reverse case, the pressure rise ~ u l d have been sceempanled by increase in the number of active vaporization centers and, consequently,
in the intensity of spraying associated
with collapse of vapor bubbles. It has been also established that the intensity of drop carry-over is affected by the design of the wick. The lowest i~tensity was observed with one-layer screens placed on the heating surface. With thicker wicks, the spraying increased, which was also observed by the authors of ~33- The larger arthery clearance for passage o f liquid made f o r carry-over.
increase in the drop
Discussion Drop formation in liquid evaporation from the plane interface was noted in ~ , ~ . A change in the vapor parameters with increase in the heat transfer rate occurs in such a fashion %bat the vapor becomes more and more superheated and, under certain conditions, the degree of supersaturation reaches so a high valua that in the vicinity of the interface there occurs a spontaneous Jump in homogeneous condensation which is accompanied by formation of drops. However, this effect is important only at Mach numbers close to unity, i.e. at conventional heat loads,with vapor velocit~ not exceeding 1-2 m~s, the fommation of drops cannot be attributed to homogeneous condensation of the supersaturated vapor.
342
V.I. Tolubinsky, et al.
Vol. 5, No. 6
FIG. 2 To determination of meniscus radius. Expulsion of liquid drops was also observed in the process of drying capillary-porous bodies ~6~ and was caused by penetration of the vapor phase, formed inside a porous body, through the liquid in the above-lying layers. In evaporation from the free surface of menisci, the carryover of drops is caused by other reasons. Let us consider one of the possible mechanisms for the drop carry-over. The radius of a meniscus (Fig.2) formed in the cell of a capillary structure is determined from
Rm=R+r (1-sin
)
(i)
sin( %o - 9 ) Non-uniform supply of liquid into separate cells due to different cross-sections of the arthery channels or non-uniform heat fluxes at the heating surface lead, as a result of evaporation, to recession of a meniscus liquid, i.e. according to dius. As a result, between ferent liquid supply there
in that very pore which is short of (1) to a change in the meniscus rathe two adjacemt menisci with difwill appear the forces which will be
directed towards the highest curvature of the profile. This will
Vol. 5, No. 6
LIQUIDEVAFOFUiTICNE'FCMCAPILL?GUsmaK7IuREs
343
cause displacement of the liquid partition between the menisci to the side of the recessed one (its radius, according to (l), is smaller). As the partition moves, the difference between the menisci curvatures is reduced, i.e. the moving force decreases. As a result of such a disturbing effect, the inertia forces may effect vibrations of the partition which lead to fluctuation of the liquid flowrate in the whole structure of the wick. This was olearly 0bserve.dboth in experiments with water and organic liquids. The significant faot is that fluctuations were also observed at very low heat flux densities when liquid pool boiling on pure surface was as yet impossible. As a result of the partition vibration, irregularities appear on the surface of the meniscus from the crests of which the flow of vapor, formed by liquid evaporation in the cell, tears away the assemblies of liquid particles. Captured by the vapor flow, these assemblies,are driven out of the cell in the direction of vapor motion. During wandering, they collide, form larger complexes (drops) and these can be observed visually. At first glance, the velocity of drops cannot exceed the vapor velocity at the outlet from the cell. However, the drops are formed in those pores Where the rate of evaporation, due to thinning of the film in the middle portion of the meniscus, exceeds the surface-average one. Thinning of the liquid film increases the heat transfer rate in the pore and this causes transfer of heat from the surrounding cells with reduced heat removal. Therefore the drops may have higher velooity than the reduced average vapor velocity. The velocity, dimensions and the flight path of dmps were determined with the help of a high-speed motion picture camera CKC-m-16. The filming was caried out in transmitting light, The dimensions of drops were determined by comparing them with a standard positioned in the view of the objective above the wick surface. The velocity of a drop was determined on the initial section of its flight by comparing the path traversed by the drop (from its projection onto the screen) with the time this path has been traversed ( from the number of pictures at
344
V.l. Tolubinsky, et al.
Vol. 5, No. 6
Wd /,0
/
o,6
l
o,:.
o,6
o'/ e-2
t,o
FIG. 3 Average velocity of 0.18-0.2 mm-dia drops vs vapor velocity at outlet from cells: I, perforated plate with 0.5 mm-dia apertures and 0.~8 surface porosity; 2, brase screen wick with 0.82 x 0.82 mm cells and 0.53 surface porosity. the known speed o f film4ng). The experimental data obtained (Pig.3) confirm the assumption that drops are formed in those pores where there is insufficient supply of liquid or where heat flux densities are high. The above mechanism of drop carry-over is realized not only in screened wicks, but also in perforated plates and metal-fibrous wicks. It is clear that evaporation from the interraces of single menisci at the same heat flux densities cannot be aooompamied by drop carry-over of liquid. As i% was noted above, the intensit~ of spraying is associated with the vapor velocity and, oonsequemtly, with the heat flux and vapor densities. This is the explanation to the fact that the i~tensity of drop formation increases with dectease in pressure and increase in heat load. The departure of the cell shape from an ideal toroidal one in screened structures leads to distortion of the meniscus
Vol. 5, NO. 6
LIQUID EVAI~RATION FROM CAPTI',I",~d~~
S
345
shape and to a situation when in one and the same meniscus there are sections of different curvatures which conduces to the onset of disturbances
and drop formation.
The wicks made
of screens with large cells spray small amounts of liquid since the shape of the meniscus is not so largely distorted in the process of vapor generation as in fine-cell
screens.
Drop carry-over of liquid creates shortage of the working fluid in the vapor generation zone of the heat pipe, i.e. results in its earlier drying-out and ,thus, to emergency operation. A decrease in pressure (increase in the intensity of spraying) develops such conditions when, despite the increase in surface tension, the heat of vaporization
and liquid density,
the evaporator may dry out earlier (at lower heat flux densities) than at high pressures. Then the heat transfer rate will decrease,which is clearly seen in Fig.~.
cc
I
)
"
I I
@
v
o
!
O
c
I
0 0
8
o-l
o
@-2 0
tOO
"
I 800 FIG. g
Water evaporation heat transfer rate vs heat flux density. Brass-screened wick with 0.51 x 0.54 mm cells: I, pressure 0.05 MPa; 2, pressure 0.~ MPa.
346
V.I. Tolubinsky, et al. The drop carry-over is responsible
Vol. 5, No. 6 for the effect of the
heat pipe evaporator orientation in space on the limiting heat flux densities. For heat pipes with a horizontal evaporator , when the greater portion of the ejected liquid returns under gravity back to the wick surface in the heating zone~ this effect is the lowest. However,
even in this ease, a portion of
the ejected drops will be captured by the vapor flow and driven away from the zone of heating. The higher the vapor flow velocity, the less amount of liquid will return back to the surface. Conclusion I. It has been established
that when heat transfer from liquid-
laden porous materials is intense, there is no boiling but evaporation from the surface of menisci of capillary pores. 2. Evaporation from the surface of menisci of capillary structures is accompanied by drop carry-over, i.e. spraying of liquid due to non-uniform hydrodyr~mic
properties
of struc-
tures. 3. Drop carry-over may lead to shortage of liquid in the evaporation zone and, as a result, to superheating of the heat pipe walls. Nomenclature meniscus radius, m ; R
half-width of capillary-structure
cell, m ;
r
wire radius of screen or radius of rounded-off
edge
of perforated screen aperture, m ; @
contact angle
;
angle determining the place of meniscus wire of screen
~v
contact with
;
average vapor velocity at outlet from capillary structur~ cell, m/s
;
Vol. 5, No. 6
wd
LIQUID EVAPORATION FROM CAPILLARY ~
347
average liquid drop velocity at outlet from capillary structure cell, m/s ;
q
heat flux density, kW/m 2 ; heat transfer coefficient, kW/m2K .
References I.
V.I.Tolubinsky, V.A.Antonenko and Yu.N.Ostrovsky, Destruction of immovable boiling liquid films, in: Thermal Physics and Thermal Engineering vyp.32, 47 (1977).
2.
A.Abhat and R.A.Seban,Boiling and evaporation from heat pipe wicks with water and acetone, Trans.ASME, Set.C, J. Heat Transfer 96 ,74 (1974).
3.
G.I.Voronin,A.V.Revyakin and V.Ya.Sasin, Low-Temperature Heat Pipes for Flying Vehicles, Mashlnostroenie Press, moscow (1977).
~.
T.M.Muratova and D.A.Labuntsov, Kinetic analysis of evaporation and condensation, Teplofiz.Vys.Temp. 7, 5, 959(1969).
5.
D.A.Labuntsov and A.P.Kryukov, Intense evaporation processes, Teploenergetika No.4, 8 (1977).
6.
A.V.Luikov and L.LoVasiliev, Heat and mass transfer in capillary-porous bodies blown by a rarefied gas flow, in : Low-Temperature Heat and Mass Transfer, 5 (1970).
DROP CARRY-OVER PHEN0~ENON IN LIQUID EVAPORATION PROM CAPILLARY STRUCTURES V.I.Tolublnsky, V.A.Antonenko, Yu.N.0stzovsky, E .N. She vchuk Institute of Engineering Thermophysics,Kiev,USSR
(C~,.~nicated by OoG. Martynenko and R.I. Soloukhin)
ABSTRACT
It has been experimentally established that heat transfer from the surface of the liquid-laden capillary-porous material is accomplished by evaporation from the free surface of menisci and is accompanied by carryover of drops of the womkimg fluid. The reason for this phenomemon is non-unifoxmity of liquid supply towards separate cells of the structure or non-unifommity of thermal conditions at the heating surface. The spraying intensity depemds on the geometrical ohazacteristios of the capillary structure, physical properties of the liquid, and pressure.
Ex~e ,riment,al The paper presents the results of an experimental study of the vapor formation mechanism in capillary structures of heat pipe wicks. The experiments were oond-,oted on the set-up, described in fl~, with the workin~ element in the form of a copper %herm~l wedge which imitated the evaporation region of a heat pipe (Pig. I). The stwuoture investigated was closely attached to a 28 ramdid enf-faoe heating surface of the wedge. The height of liquid in the chamber was kept 1-2 mm below the level of the heating smrfaee, with the contour of the wick being completely immersed in liquid. Thus, Just as in heat pipes, the cooling liquid was supplied to the heating surface by capill~ry forces only. 339
340
V.l. Tolubinsky, et al.
Vol. 5, No. 6
8
i m
FIG. i Schematic diagram of the set-up: I, thermal wedge ; 2, capillary structure. The heat flux density and the heating surface temperature were determined by the temperature gradient along the body of the wedge. The test chamber was provided Wi+~ vlewi~g windows of quartz glass for visual observations, graphic inspe orlon.
cinema- and photo-
The experiments were carried out with distilled water in the pressure range frc~ 0.02 to 0.4 ~ a and with buthyl alcohol, normal h e p ~ i n , acetone and benzole at a~mospheric pressure in capillary structures which are most characteristic of the heat pipe wlcks~ i.e. screensp metal fibres and perforated screens ( 35 types in all ). Direct visu81 observations of the pxocesses occurring on the surface of porous specimens have shown that at h~gh heat flux densities (for e~ample, for water at q > 150-200 kW/m 2) liquid evaporates from the surface of the menisci of capillary pores with no boiling. Even at the pressure of 0.02 KPa and the heat flux density of 700 kW/m 2, vapor bubbles do not form on the surface of the wicks ( t ~ % can allow this heat load, of course). In this case, the curvilinear surfaces of menisci is clearly observed.
Vol. 5, No. 6
LIQUID EVAPORATION FROM CAPr~ZARY ~
341
It has been established in the course of the experiments that evaporation from the free surface of menisci in capillary structures is accompanied by capillary carry-over of liquid. Expulsion of liquid from the wicks of heat pipes was noted long ago [2,3J, but was related to collapse of vapor bubbles in boiling. The experiments have shown that the intensity of drop carry-over depends on pressure and increases with decrease in the latter. Under vacuum, the carry-over is such that often makes visual observations difficult. However, already at 0.~ MPa, the carry-over is practically absent. This, by the way, once more confirms the absence of boiling in pores of capillary structures, since in the reverse case, the pressure rise ~ u l d have been sceempanled by increase in the number of active vaporization centers and, consequently,
in the intensity of spraying associated
with collapse of vapor bubbles. It has been also established that the intensity of drop carry-over is affected by the design of the wick. The lowest i~tensity was observed with one-layer screens placed on the heating surface. With thicker wicks, the spraying increased, which was also observed by the authors of ~33- The larger arthery clearance for passage o f liquid made f o r carry-over.
increase in the drop
Discussion Drop formation in liquid evaporation from the plane interface was noted in ~ , ~ . A change in the vapor parameters with increase in the heat transfer rate occurs in such a fashion %bat the vapor becomes more and more superheated and, under certain conditions, the degree of supersaturation reaches so a high valua that in the vicinity of the interface there occurs a spontaneous Jump in homogeneous condensation which is accompanied by formation of drops. However, this effect is important only at Mach numbers close to unity, i.e. at conventional heat loads,with vapor velocit~ not exceeding 1-2 m~s, the fommation of drops cannot be attributed to homogeneous condensation of the supersaturated vapor.
342
V.I. Tolubinsky, et al.
Vol. 5, No. 6
FIG. 2 To determination of meniscus radius. Expulsion of liquid drops was also observed in the process of drying capillary-porous bodies ~6~ and was caused by penetration of the vapor phase, formed inside a porous body, through the liquid in the above-lying layers. In evaporation from the free surface of menisci, the carryover of drops is caused by other reasons. Let us consider one of the possible mechanisms for the drop carry-over. The radius of a meniscus (Fig.2) formed in the cell of a capillary structure is determined from
Rm=R+r (1-sin
)
(i)
sin( %o - 9 ) Non-uniform supply of liquid into separate cells due to different cross-sections of the arthery channels or non-uniform heat fluxes at the heating surface lead, as a result of evaporation, to recession of a meniscus liquid, i.e. according to dius. As a result, between ferent liquid supply there
in that very pore which is short of (1) to a change in the meniscus rathe two adjacemt menisci with difwill appear the forces which will be
directed towards the highest curvature of the profile. This will
Vol. 5, No. 6
LIQUIDEVAFOFUiTICNE'FCMCAPILL?GUsmaK7IuREs
343
cause displacement of the liquid partition between the menisci to the side of the recessed one (its radius, according to (l), is smaller). As the partition moves, the difference between the menisci curvatures is reduced, i.e. the moving force decreases. As a result of such a disturbing effect, the inertia forces may effect vibrations of the partition which lead to fluctuation of the liquid flowrate in the whole structure of the wick. This was olearly 0bserve.dboth in experiments with water and organic liquids. The significant faot is that fluctuations were also observed at very low heat flux densities when liquid pool boiling on pure surface was as yet impossible. As a result of the partition vibration, irregularities appear on the surface of the meniscus from the crests of which the flow of vapor, formed by liquid evaporation in the cell, tears away the assemblies of liquid particles. Captured by the vapor flow, these assemblies,are driven out of the cell in the direction of vapor motion. During wandering, they collide, form larger complexes (drops) and these can be observed visually. At first glance, the velocity of drops cannot exceed the vapor velocity at the outlet from the cell. However, the drops are formed in those pores Where the rate of evaporation, due to thinning of the film in the middle portion of the meniscus, exceeds the surface-average one. Thinning of the liquid film increases the heat transfer rate in the pore and this causes transfer of heat from the surrounding cells with reduced heat removal. Therefore the drops may have higher velooity than the reduced average vapor velocity. The velocity, dimensions and the flight path of dmps were determined with the help of a high-speed motion picture camera CKC-m-16. The filming was caried out in transmitting light, The dimensions of drops were determined by comparing them with a standard positioned in the view of the objective above the wick surface. The velocity of a drop was determined on the initial section of its flight by comparing the path traversed by the drop (from its projection onto the screen) with the time this path has been traversed ( from the number of pictures at
344
V.l. Tolubinsky, et al.
Vol. 5, No. 6
Wd /,0
/
o,6
l
o,:.
o,6
o'/ e-2
t,o
FIG. 3 Average velocity of 0.18-0.2 mm-dia drops vs vapor velocity at outlet from cells: I, perforated plate with 0.5 mm-dia apertures and 0.~8 surface porosity; 2, brase screen wick with 0.82 x 0.82 mm cells and 0.53 surface porosity. the known speed o f film4ng). The experimental data obtained (Pig.3) confirm the assumption that drops are formed in those pores where there is insufficient supply of liquid or where heat flux densities are high. The above mechanism of drop carry-over is realized not only in screened wicks, but also in perforated plates and metal-fibrous wicks. It is clear that evaporation from the interraces of single menisci at the same heat flux densities cannot be aooompamied by drop carry-over of liquid. As i% was noted above, the intensit~ of spraying is associated with the vapor velocity and, oonsequemtly, with the heat flux and vapor densities. This is the explanation to the fact that the i~tensity of drop formation increases with dectease in pressure and increase in heat load. The departure of the cell shape from an ideal toroidal one in screened structures leads to distortion of the meniscus
Vol. 5, NO. 6
LIQUID EVAI~RATION FROM CAPTI',I",~d~~
S
345
shape and to a situation when in one and the same meniscus there are sections of different curvatures which conduces to the onset of disturbances
and drop formation.
The wicks made
of screens with large cells spray small amounts of liquid since the shape of the meniscus is not so largely distorted in the process of vapor generation as in fine-cell
screens.
Drop carry-over of liquid creates shortage of the working fluid in the vapor generation zone of the heat pipe, i.e. results in its earlier drying-out and ,thus, to emergency operation. A decrease in pressure (increase in the intensity of spraying) develops such conditions when, despite the increase in surface tension, the heat of vaporization
and liquid density,
the evaporator may dry out earlier (at lower heat flux densities) than at high pressures. Then the heat transfer rate will decrease,which is clearly seen in Fig.~.
cc
I
)
"
I I
@
v
o
!
O
c
I
0 0
8
o-l
o
@-2 0
tOO
"
I 800 FIG. g
Water evaporation heat transfer rate vs heat flux density. Brass-screened wick with 0.51 x 0.54 mm cells: I, pressure 0.05 MPa; 2, pressure 0.~ MPa.
346
V.I. Tolubinsky, et al. The drop carry-over is responsible
Vol. 5, No. 6 for the effect of the
heat pipe evaporator orientation in space on the limiting heat flux densities. For heat pipes with a horizontal evaporator , when the greater portion of the ejected liquid returns under gravity back to the wick surface in the heating zone~ this effect is the lowest. However,
even in this ease, a portion of
the ejected drops will be captured by the vapor flow and driven away from the zone of heating. The higher the vapor flow velocity, the less amount of liquid will return back to the surface. Conclusion I. It has been established
that when heat transfer from liquid-
laden porous materials is intense, there is no boiling but evaporation from the surface of menisci of capillary pores. 2. Evaporation from the surface of menisci of capillary structures is accompanied by drop carry-over, i.e. spraying of liquid due to non-uniform hydrodyr~mic
properties
of struc-
tures. 3. Drop carry-over may lead to shortage of liquid in the evaporation zone and, as a result, to superheating of the heat pipe walls. Nomenclature meniscus radius, m ; R
half-width of capillary-structure
cell, m ;
r
wire radius of screen or radius of rounded-off
edge
of perforated screen aperture, m ; @
contact angle
;
angle determining the place of meniscus wire of screen
~v
contact with
;
average vapor velocity at outlet from capillary structur~ cell, m/s
;
Vol. 5, No. 6
wd
LIQUID EVAPORATION FROM CAPILLARY ~
347
average liquid drop velocity at outlet from capillary structure cell, m/s ;
q
heat flux density, kW/m 2 ; heat transfer coefficient, kW/m2K .
References I.
V.I.Tolubinsky, V.A.Antonenko and Yu.N.Ostrovsky, Destruction of immovable boiling liquid films, in: Thermal Physics and Thermal Engineering vyp.32, 47 (1977).
2.
A.Abhat and R.A.Seban,Boiling and evaporation from heat pipe wicks with water and acetone, Trans.ASME, Set.C, J. Heat Transfer 96 ,74 (1974).
3.
G.I.Voronin,A.V.Revyakin and V.Ya.Sasin, Low-Temperature Heat Pipes for Flying Vehicles, Mashlnostroenie Press, moscow (1977).
~.
T.M.Muratova and D.A.Labuntsov, Kinetic analysis of evaporation and condensation, Teplofiz.Vys.Temp. 7, 5, 959(1969).
5.
D.A.Labuntsov and A.P.Kryukov, Intense evaporation processes, Teploenergetika No.4, 8 (1977).
6.
A.V.Luikov and L.LoVasiliev, Heat and mass transfer in capillary-porous bodies blown by a rarefied gas flow, in : Low-Temperature Heat and Mass Transfer, 5 (1970).