Flow boiling in microgravity - a review

7/28/2019 Flow boiling in microgravity - a review

1/18

GRAVITY EFFECTS ON FLOW BOILING

GAUTAM WUDDI

ABSTRACT

This review of Gravity effects on Flow Boiling attempts to summarize the mostpromising results of the research performed in this area. While a reasonable amount ofdata has been accumulated over the years for microgravity, there is very little for hyper-gravity. This may be because the major focus of most of the investigations has been toclarify flow mechanisms and behaviour in reduced gravity environments. Another reasonis the sheer expense and difficulty of collecting quality data in parabolic flights. Futureexperiments on the International Space Station might resolve some of the difficultiesinvolved, besides giving very high quality data.

INTRODUCTION

The quantum jump in research being conducted in space environments and theadvanced microprocessor technology being used in endurance military aircraft hasexposed the need for better heat transfer methods than the single phase cooling thusfar adopted. The focus has now fallen upon heat transfer using two phase flow coolingmethods wherein both the sensible as well as latent energy of the fluid or refrigerant canbe leveraged. Two phase flows are also very conducive to transporting heat at nearlyisothermal conditions over long distances. Both of these characteristics give them very

high heat transfer coefficients. The fact that the latent heat is being utilized allows us toreduce the volumetric flow rate and thus the pumping requirements, which is critical inthe applications mentioned above.

The major parameters that have been considered in this study are the differentflow regimes that occur in a microgravity environment, the criteria for transition betweendifferent flow regimes, the heat transfer coefficients and correlations for the frictionalpressure drop and the critical heat flux.

Basic Terminology:

For a channel with cross-sectional area A, the mass flux or mass velocity G isgiven by G = (m/t)/A. The volume fraction is the ratio of the volume of a phase overthe the total volume of flow. If the volume consists of a cross sectional area times thelength, the volume fraction may be simplified to an area fraction. The vapor phasevolume fraction is referred to as the void fraction, denoted by or . The slip is theratio of the phase velocities - if both phases are moving with the same velocity, i.e., slipis equal to 1, then the flow is referred to as homogenous.


2/18

The equilibrium quality ((h - hf)/hfg) may be thought of as a measure of the degreeof superheating or sub-cooling of a fluid. In conditions where thermodynamic equilibriumexists between the phases, the quality corresponds to the flow fraction of the vapor; itcan also be referred to by the term dryness fraction.

The volumetric flux of a phase is defined as the volumetric flow rate of the phaseover the total flow area. Physically, it has the units of velocity and may be thought of asthe velocity that a phase has if it is flowing through the channel alone. It is also morecommonly referred to as the superficial velocity.

Several flow regime maps have been developed for terrestrial gravity conditions,which help with keeping the flow in a recommended regime during design of equipment.Usually bubbly and annular flow are preferred and slug flow is avoided since it causesvibrations in the channels which may result in structural damage.

Dimensionless numbers:

Jakob number: It is the ratio between the sensible and the latent heat absorbedduring a phase change process.

Ja = Cp(Ts - Tsat)/hfg

Bond number: It is the ratio between the gravitational and the surface tensionforces.

B = d2/

Weber number: It is the ratio between the forces of inertia and surface tension.

We = U2d/

Reynolds number: It is the ratio between the inertial and viscous forces.

Re = Ud/

Suratman number: It is the ratio of surface tension to the momentum dissipationin a fluid. It is also called the Laplace number and is used as a characteristic length inboiling.

Su = La = L/2.

Considering the superficial phase velocities instead of the mean flow velocities inthe above dimensionless quantities give rise to the superficial dimensionless numbers,denoted with a subscript S.

2


3/18

THEORETICAL INVESTIGATIONS

The flow is said to be in the bubbly flow regime when the size of the vaporbubbles is less than or equal to that of the diameter of the tube. The flow is designated

as slug flow when the size of the bubbles are greater in length than the diameter of thetube. Annular flow is the condition where the liquid never bridges the tube [1]. Althoughthere has been one more regime - frothy slug annular flow or transition regime -reported in microgravity flows, the three mentioned above are the widely accepted. The transition of flow from bubbly to slug occurs when the bubble concentrationand size is such that adjacent bubbles come into contact. The conventional treatment ofbubble coalescence requires that there be a liquid layer trapped between the twocoalescing bubbles, and when the liquid film drains out, over a certain time, aninstability mechanism will result in film rupture and bubble coalescence [2]. In amicrogravity environment, the only forces that influence motion and coalescence of

bubbles is the motion induced by turbulence. Kamp et al.[3] conducted a study in whicha numerical model for bubble coalescence on the basis of the collision frequency anddrainage time are verified using experimental results conducted in a microgravityenvironment. A conclusion of their investigation is that bubble growth due tocoalescence between inlet and outlet diminishes with increasing liquid flow rate.

Slug flow is characterized by a plug of liquid, which is followed by a long Taylorbubble. The liquid plug may have smaller bubbles dispersed in it. The diameter of theTaylor bubble is close to that of the tube diameter and liquid is forced to flow around thebubble. If a co-ordinate system which moves along with the Taylor bubble is considered,the liquid film around the bubble flows backwards - whether for terrestrial gravity or for

microgravity conditions - and a conventional force analysis may be performed, such asthat for vertical upward flow under gravity, with the surface tension taken intoconsideration[4]. A numerical solution using the Runge-Kutta method reveals that thesurface tension may be neglected in the range where the film thickness is less thanabout one-third of the pipe radius. The surface tension cannot, however, be neglected atthe nose of the Taylor bubble. From the knowledge of the film thickness profile,estimation of the pressure drop can be performed by considering a control volumearound a slug.

Pu = uglu + (sD/A)lsfSf/A dz

where the average slug density is u = uG + (1 - u) L.

Dukler also attempted to theoretically estimate the values of all the parametersfor annular flow, using a control volume approach. He then extended the flow regimemap for 1-g to microgravity.

3


4/18

Data from a microgravity experiment in a 6 mm tube plotted on a Dukler mapFigure from Celata et al. [30]

A theoretical study by Eastman et al. [5] reported that flow pattern transitions indifferent gravity fields could be reasonably well predicted using the criteria of Weismanet al. [6]:

G = B (1/x) (x/1-x)0.2232 g0.4107 for the transition from intermittent to annular

G = C/(1-x) g0.25 for the transition from annular to dispersed flow.

Karri and Mathur [7] extrapolated the 1-g models of Taitel et al. and Weismen etal. for horizontal and vertical flows to microgravity. The modified models predicted thatthe transition boundaries would move towards lower superficial velocities of both thephases as the gravity level was reduced. At a gravity level of 10-5g, the modified flowregime maps showed that there existed only three flow regimes: bubbly, intermittent andannular.

An extensive theoretical and experimental study of two phase frictional pressuredrop in tubes has been conducted and a number of correlations have been proposed fornormal gravity. The methods developed so far can be classified into two categories:homogenous flow and separated flow. The former treats two phase flow as a pseudo

single phase flow with suitably averaged properties of the liquid and vapor phases. Thelatter considers the two phase flow to be essentially flow in two different pipes, with thevelocity of the phase constant in its pipe. Two phase flow multipliers are a characteristicof this approach. Correlations for terrestrial pressure drop data have been extended tomicrogravity flow, by factoring in the reduction in the gravitational force, and consideringthe usually neglected surface tension. Under conditions of microgravity, the phasedistribution is symmetrical and the slip ratio is very small, though there is agreementabout the latter only for bubbly flow. Although this is a good starting point, experimental

4


5/18

studies are needed to confirm the validity of extending terrestrial designed correlationsto microgravity.

For a two phase flow system, under reduced gravity conditions, the reduction ofbuoyancy has two effects: i. decreases the liquid fraction due to a decrease in the slip

ratio (leading to a higher liquid velocity, and consequently a higher pressure loss);ii. reduce the turbulence amplification induced by bubble movement. The balancebetween the two effects will determine the frictional pressure gradient [8]. When the flowis dominated, to a large extent, by inertia, no significant changes in pressure gradientdue to gravity or the lack of it were observed.

EXPERIMENTAL INVESTIGATIONS

FLOW REGIME

An early observation and classification of the various flow regimes in amicrogravity environment was done by Zhao and Rezkallah [9]. They grouped the flowregimes into three major regions: a surface tension dominated region, an inertiadominated region and a transitional region in between. The bubbly and slug flows wouldbe the surface tension dominated regimes, the transitional region would comprise of thefrothy slug annular flow and the inertia dominated region was the annular flow. Theydistinguished the bubbly and slug flows using the void fraction - based on the superficialvelocities; when the void fraction was smaller than 0.18, bubbly flow was said to exist,when larger, the flow pattern would be a slug flow. Since, in this flow condition, thesurface tension force is dominant, the "Taylor" slugs observed had a spherical nose and

so did the smaller bubbles between the slugs. Close visual observation reveals that thedistance between the smaller bubbles and the slugs remains constant throughout theflow regime. This indicates that there is negligible slip, if at all existent, in the bubbly/slug flow regimes. As the gas flow rate is gradually increased, the increasing density ofthe slugs breaks them up into smaller bubbles, which are entrained in the flow. At thispoint, there is a balance between the surface tension and the inertia forces and it givesrise to the frothy slug annular flow regime. In this regime, the liquid flows at the wall ofthe tube, while the gas flows in the center with frequent appearances of frothy slugs init. As the gas flow rate is further increased, inertia dominates and annular flow - liquid atthe wall and uninterrupted gas flow in the center - ensues.

An investigation by Macgillivray et al. [10] on the variation of annular flow filmthickness with gravity - with a water-air mixture, for vertical upward flow - concluded thatthe effect of gravity on the average film thickness values is minimal.

5


6/18

Flow regimes in microgravity - Figure from Valota et al. [17]

The Weber number is defined as the ratio of inertial forces to the surface tension.

Given the absence of gravitational effects i.e. buoyancy, the Weber number is oneparameter which can describe the criteria for microgravity flow transitions. Rezkallah[11] plotted the Weber numbers in terms of the liquid and vapor velocities for the water-air data of Elkow & Rezkallah and the water-air and glycerine/water-air data sets ofBousman. On the basis of this plot, Rezkallah specified the gas phase Weber numberfor the transition from bubbly/slug to transitional flow as being around 2, and that for thetransition to fully developed annular flow to occur at a gas phase Weber number of 20.Both the liquid viscosity and the diameters of the tube were found to have a minimalinfluence on the transitions.

Flow pattern map on the basis of actual liquid and vapor Weber numbers

Figure from Rezkallah [11]

6


7/18

However, Parang and Chao observed that the Weber number could not predictthe transition data accurately at higher liquid phase velocities [12]. They also contendedthat, among all the studies that had been performed, the range of Weber numbers hadbeen varied only by varying the velocity of the flow but not the fluid properties. It is alsohighly unlikely that the same force balance between inertial and surface tension forces

would hold good in flow patterns as varied as bubbly, slug and annular flows. Based onthe data taken from Bousman [13], they suggested that, for the transition from slug toannular flow, the correct scaling parameter would be Weg/Rel and that the transitionwould occur at 10-3. For the transition from bubbly to slug flow, the parameter was Weg/Rel1.8 and the transition occurred at 5x10-8. They concluded that their scalingparameters would capture the balance between turbulent shear and gas inertia. Jayawardena et al., using dimensional analysis, theorized that the transitionsshould depend on the liquid and gas phase superficial velocity Reynolds numbers andthe liquid Suratman number [14]. Experimental data, along with some empiricalparameters, were used to derive the following boundaries for transition from slug to

annular flow.

ReSG/ReSL = K2Su- for Su < 106

ReSG = K3Su2 for Su > 106

where the liquid Suratman number SuL = Re2SL/WeSL K2(= 4641.6) and K3(= 2 x 10-9) are empirical parameters.

Microgravity flow pattern maps for Su106

Figure from Sen [16] Zhao and Hu extended the drift flux model of Reinarts and proposed to use thesuperficial Weber numbers of the phases, in dimensionless form, along withexperimentally determined values for the empirical parameters C0 and K [15]. Thismodel predicts the boundaries quite well in the bubbly flow regime but is notsubstantiated with data in the slug flow regime.

7


8/18

A theoretical investigation by Sen on slug to annular flow transition reinforcesJayawardane's results and attempts to provide a physical basis for it [16]. For thetransition from slug flow to annular flow, a higher gas flow rate, resulting in a higherReSG, is required. It is accepted that as the gas phase Reynolds number increases, thewave height decreases and vice versa. Expressing the same in non-dimensional terms,

the wave height increases as the ratio of ReSG/ReSL decreases. As the Suratmannumber increases, for a constant tube diameter, the surface tension must increase,which should result in a decrease in the wave height or a smoother gas liquid interface.The model proposed by Jayawardena et al. was found to predict the transitionboundaries quite accurately.

Valota et al. conducted experiments using a capacitance sensor for void fractionmeasurements to determine if the statistical parameters obtained from the fluctuation ofthe void fraction measurements could be used to identify the flow regimes [17]. Theyreported that the variance and the signal to noise ratio (smaller for annular flow, largervalues for slug flow) suited that function well.

The semi-empirical void fraction models proposed by Dukler, Reinarts, Bousmanand Zhao suffer from their dependence on the empirical values of interfacial frictionfactor (C0) and drift flux distribution coefficient (K) for slug flow.

BUBBLE DYNAMICS

Cooper et al., after investigation of bubble ebullition on a vertical flat plate in alaminar up-flow of supersaturated hexane, concluded that bubble growth wasdependent primarily on the thermal diffusivity and the Jacob number, and that theinfluence of surface tension and viscosity were negligible [18]. Wang et al. reported that

bubbles would slide and roll on the heater surface when the heat flux supplied wasbeyond a threshold value [19]. The average bubble velocities after departure from theirnucleation sites ranged between 80-90% of the free-stream velocity.

Ma and Chung experimentally investigated bubble dynamics in FC-72 in a droptower [20]. All system parameters and results were normalized. They reported that, inmicrogravity, the bubble's shape developed from oblong to nearly perfect spherical, withthe size being larger than that observed in earth gravity. They concluded that gravityeffects could be neglected when forced convection - inertia effects - were dominant. Asthe Reynolds number of the flow increased, they observed that the size of the bubbledecreased, the angle of its inclination with the heater surface increased and so did the

rate of bubble departure from their nucleation sites. They also reported that, at very highReynolds numbers, suppression of boiling occurred. They observed that the diameter ofa bubble during its growth was proportional to the one-third power of the time of itsgrowth and proposed a correlation for bubble growth in microgravity: D/La = c b Re-1/3t*1/3

where cb is a function of liquid-heater properties and bulk temperature.

8


9/18

At low to moderate Reynolds numbers, the frequency of bubble generation wasobserved to increase with the flow rate, but was still lower than that in conditions ofterrestrial gravity. At higher Reynolds numbers, the influence of gravity on bubblegeneration is negligible.

Bubble growth with increase of Reynolds number

V* and t* are the normalized volume and time, at departure.

The results of Ma and Chung were confirmed in an experimental investigation bySerret et al. for convective boiling between two plates separated by a distance of 1 mm.They also reported that there was a slight decrease in the average nucleation sitetemperature, which was consistent with the frequent rewetting of the surface due to

higher frequency of bubble departure [21].

Clarke and Rezkallah attempted to numerically simulate the behaviour of bubblesin a two phase flow at different Reynolds numbers of flow and validate them against theexperimental data [22]. They concluded that for increasing values of the bubble size andthe liquid Reynolds number and for lower values of the surface tension, the drift velocityof the bubble increased. This explains the tendency of the bubbles at the center to bespherical in shape than those at the walls.

HEAT TRANSFER

Misawa and Anghaie performed drop tower experiments on Freon 113 andobserved that the slip ratio in conditions of microgravity is less than one [23]. Theincreased void fraction and thereby acceleration resulted in a larger pressure drop thanthat predicted by the homogenous model. Investigations conducted aboard a KC-135aircraft by Kawaji et al. showed that there is a reduction of heat transfer rate inmicrogravity due to the formation of a thicker vapor layer on the surface of the tube [24].Flow pattern observation of subcooled Freon 113 showed that there were marked

9


10/18

differences in the shape of the bubbles in the dispersed flow regions. Reinarts et al.working with R12, reported that the condensation heat transfer coefficients atmicrogravity were 26% lower than those at 1-g conditions [25].

Saito et al. conducted investigations in parabolic aircraft with a rod shaped

heater concentric with a square channel [26]. It was observed that, under conditions ofmicrogravity, the fluid temperature above the heater rod decreases, while the fluidtemperature below the heater rod remained relatively unchanged. The wall temperatureof the heater rod increased slightly, both on the top as well as on the bottom surfaces.Unlike in conditions of gravity, the sub-coolings of the upper stream and lower streamremained fairly constant. They also reported that the local heat transfer coefficientsincreased slightly on the top of the heater rod, while those at the bottom of the heaterrod decreased slightly. The differences in the local heat transfer coefficients were stillobserved to be small, despite the large variation in the flow regimes under earth gravityand microgravity. All of these can be attributed to the diminished influence of naturalconvection at low inlet velocities. They also reported that under conditions of low inlet

velocity, the bubbles did not leave the surface of the heater but started growing largerdue either to continued heating and vaporization at the surface of the heater or due tocoalescence. As the inlet fluid velocities were increased, thus increasing the fluid inertia,the bubbles were dragged along the surface of the heater.

Ohta [27] conducted an extensive series of experiments, in parabolic aircraft,using three different inlet conditions and heat fluxes. Under conditions of (a/g)=1 andsub-cooled liquid, the upstream flow was bubbly, but, with increase in quality, italternated between froth and annular flow. For (a/g)>1, the diameter of the bubbles wasobserved to decrease, while at the same time, their velocity relative to the velocity of thebulk liquid increased. The instantaneous void fraction decreased. In microgravity, as

may be expected, the trend was reversed, with a decrease in bubble velocity, leading toan increase in the void fraction, resulting ultimately in a transition to annular flow at alower dryness fraction. For conditions where the inlet quality itself was high, annularflow - independent of gravity - resulted across the length of the tube. Under conditionsof moderate quality, leading to annular flow, (i) at low heat flux, nucleate boiling iscompletely suppressed and the heat transfer coefficient increases with gravity and viceversa; (ii) at high heat flux, the heat transfer is dominated by nucleate boiling and iscompletely independent of gravity.

Ohta also attempts to clarify the heat transfer coefficient for the annular flowregime using a method analogous to single phase flow at a heated wall, with certain

idealizations. According to him, for an annular flow regime, the heat transfer coefficientwould be defined as

= q0/(t0 - tsat)

where q0 is the heat flux at the tube wall, tsat is the saturation temperature and t0is the wall temperature.

10


11/18

Moderate quality, annular flow regime, low heat fluxFigure from Professor H. Ohta

Rite and Rezkallah, experimenting with a vertically oriented water-air test section,observed that values of the Nusselt number were lower for microgravity than for earthgravity conditions, when the quality was low. As the gas flow rate was increased,

increasing the inertia and transitioning to the annular flow regime, the earth gravity andmicrogravity data points almost coincide, implying that the differences between heattransfer for different gravity levels may be flow regime dependent [28]. They alsoreported that, for microgravity conditions, the local heat transfer coefficients at the inletwere higher than those at the outlet, unlike the behaviour in earth gravity. Inmicrogravity, the lack of buoyancy impedes the turbulence generating ability of thevapor bubbles, which then flow mainly in the center of the tube and do not affect thelaminar sub-layer. They conclude that, for two phase Reynolds numbers greater than10000, and for moderate quality (0.002), the microgravity heat transfer was greater thanearth gravity heat transfer. This might be explained by the greater frequency of bubbledetachment from the nucleation sites, leading to more turbulence in the flow, at high

Reynolds numbers.

Heat transfer experiments, in tubular test sections, using subcooled R113, werecarried out by Lui et al [29]. They reported heat transfer coefficients that were upto 20%higher in microgravity than in earth gravity.

Investigations by Celata et al. confirmed the above results [30]. They also foundthat the Dukler flow regime map could best predict the microgravity data.

11


12/18

Separate investigations by Celata et al. revealed that gravity did not have anyinfluence on the heat transfer, for annular flow. They concluded that, for a lower massflux of fluid, gravity would have a larger effect on the heat transfer coefficients [31].

CRITICAL HEAT FLUX

Ma and Chung conducted forced convection boiling experiments with FC-72 andconcluded that the CHF in microgravity is lesser than that in normal gravity at low flowrates [32]. But, as the flow rates were increased, the curves for both microgravity andgravity began to coincide, implying that gravity effects diminish with higher flow rates. Critical heat flux is a very transient phenomena, which under the most benignconditions can lead to burnout of equipment. The power budget available in a spaceenvironment is very limited, which places severe constraints on the pumping power andthereby the flow rates. While sub-cooling has been found to helpful in earth-gravity

conditions, the dimensional constraint limiting the size of condensers in a spaceenvironment makes it unfeasible. The combination of these two factors carries the riskof producing small values of CHF in reduced gravity [33].

Extensive experiments - leading to a publication rate of atleast one every twoyears - have been carried out by Mudawar and Hassan on the influence of variousparameters on the CHF in various orientations and thereby various gravity conditions.They have proposed a theory which provides an intuitive understanding of the CHFmechanism, with a predictive error of about 30%.

There are four major models that attempt to explain the phenomenon of flow

boiling CHF: boundary layer separation, bubble crowding, micro-layer dryout andinterfacial lift-off. The interfacial lift-off model proposed by Galloway and Mudawar [34] isbased on a study Hino and Ueda whose study of bubble residence time near the wallrevealed that discrete bubbles were replaced by a continuous wavy vapor layer at heatfluxes even less than the CHF. This model postulates that the liquid layer makes contactwith the walls at wetting fronts which correspond to the troughs and heat transfer due toboiling occurs at these locations. When the pressure force resulting from the interfacialcurvature is exceeded by the vapor momentum due to the vigorous boiling at thelocalized wetting fronts, the wavy layer lifts off leading to an insulating vapor blanket.When this phenomenon occurs at one wetting front, the heat that was being transferredthere will have to be transferred from some other neighboring wetting front, leading to

more vigorous boiling and hence quicker evaporation there. This chain reaction resultsin an accelerated formation of the insulating vapor layer, resulting in burnout. Mudawarand Hasan derived an expression for the lift-off heat flux and found it to be proportionalto the 1/2 which may be considered a wave curvature parameter, being theamplitude and the wavelength of the idealized sinusoidal wave. This model alsopredicts that there exists an orientation range, over which, for low velocities, theinterface is always stable, thereby producing a continuous vapor film [35]. Overall, thismodel was found to be valid for all orientations at near saturated flow at high velocities.

12


13/18

CHF trigger mechanism according to the Interfacial LiftOff modelFigures from Zhang et al. [36]

An experimental investigation of the effects of the three major forces - inertia,body force and the surface tension force - on the flow boiling CHF revealed that forconditions of saturated flow and velocities below 0.2 m/s, the CHF is very sensitive tothe orientation of flow. The CHF was found to be much less sensitive to orientation at

velocities higher than 0.5 m/s, in concurrence with other studies. Mudawar and Hassanalso compared their data with those predicted by existing correlations and found that theMudawar and Maddox correlation predicted the data well for subcooled flow, whereasfor saturated flow, the Sturgis and Mudawar model was to be preferred.

An investigation of the trigger mechanism of flow boiling at CHF performed byZhang et al. shows that the Interfacial LiftOff model accurately describes the CHFmechanism in both lunar gravity as well as microgravity [36]. They performed theirexperiment controlling the heat flux as a percentage of the CHF, which allowed them tobetter visualize the vapor layer formation. In addition to confirming the results of earlierstudies, they also concluded that, at flow velocities of about 1.5 m/s, inertia effects

exerted dominance and the effect of gravity or the lack of it could be entirely neglected,which means that, if the flow rate could be maintained above 1.5 m/s, equipmentdesigned for use in earth gravity could safely be used in microgravity as well.

The extension of any model to sub-cooled flow is complicated by the variation ofthe bulk liquid enthalpy along the length of the heated surface and the partitioning of thewall energy between the latent and the sensible heats. Zhang et al. modified theInterfacial Liftoff model for sub-cooled flow, introducing a heat utility ratio - defined as

13


14/18

the fraction of the surface heat flux that converts liquid at the vicinity of the wall and atthe bulk liquid temperature, to vapor. A constant value of 0.5 was recommended for theinterfacial friction coefficient. The resulting expression for the value of the CHF for sub-cooled flow boiling was found to agree with the experimental results within an errorrange of +-25% [37].

PRESSURE DROP

A pioneering investigation on pressure drop of gas liquid flow in microgravity wasconducted by Heppner et al. For a water-air fluid flow in a horizontal pipe, they reportedthat the pressure drop in microgravity was higher than that at terrestrial gravity. Chen etal. reported - for the same dryness fraction, of saturated R114 - that the pressure dropwas greater - by about 40% - in microgravity than in earth gravity conditions [38].

An experimental investigation by Colin et al. revealed that for conditions ofmicrogravity, pressure drop were strongly affected by the tube diameter [39]. They

reported that, for bubbly turbulent flow, in tubes of diameters 19 and 40 mm, the semi-empirical friction factor fp = 0.079 Re-1/4 correctly predicted the friction factor. However,for slug flow, the above equation under-predicts the friction factor for the 19 mm tube,while correctly predicting fp for the 40 mm tube. They also observed that, for tubes ofsmaller diameters, the friction factor was nearly proportional to the inverse of theReynolds number, although 8 to 10 times greater. They also reported that the differencebetween the experimental friction factor and that predicted using the Poiseuillerelationship increased when the Reynolds number was decreased. Using an estimate of the void fraction to determine the frictional pressure drop,Zhao and Rezkallah, testing an air-water mixture, concluded that the pressure drop in

microgravity conditions was slightly more than that at earth-gravity conditions, thedifferences between the two ranging from 1 to 14%. Plots of the two phase multipliervalues versus the quality for both microgravity and terrestrial gravity conditions werefound to coincide, for the same gas quality, supporting their observations. A possiblereason for the great difference between the results of this investigation and that of Chenet al. and Colin et al. might be that the flow velocities were much higher than that in theearlier ones. The average Reynolds number of the mixture was reported to be around104, putting it firmly in the turbulent flow regime. Another major reason for the differenceis that the earlier investigations were conducted for a horizontal pipe, wherestratification of flow would occur in terrestrial gravity conditions, whilst the latter was forvertical upward flow.

Investigations by Ohta revealed that the pressure drop increases with thesuperficial velocities in microgravity. According to Ohta, for an annular flow with a vaporcore, the interfacial friction factor may be defined as a function of the gravity, mass flowand the quality as follows: fi/fi0 = 1 + 0.08(1-x/x)0.9 Fr-1 : 0< a/g 2.

14


15/18

In the above equation, for fully vapor flow, the interfacial friction factors are equal(fi1g = fi2g = fi0), as might be expected. Using the Chisholm and Laird correlation for earthgravity conditions, Ohta extrapolates to find the interfacial friction factor for conditions ofmicro and hyper gravity. The friction factor was observed to be proportional to gravityand the effect of gravity on the friction factor was reduced with an increase in the quality

and thereby the mass velocity of vapor flow.

Zhao et al. conducted experiments aboard the Mir space station in which theycompared the pressure drops of two phase flow with some common correlations [40].They concluded that the Friedel model provided relatively better agreement with theexperimental results.

A comparison by Fang et al. of the predictive capability of the various correlationsto microgravity data revealed that the McAdams et al., Chisholm and Muller-Steinhagenand Heck performed best [41]. They also reported that the Zhao and Rekallah verticalflow data was reasonably well predicted by most of the correlations, which were defined

for horizontal flow, implying that the effect of orientation on the two phase frictionalpressure drop was minimal. They concluded that the practice of extending terrestrialgravity correlations to predict microgravity behaviour would be reasonable up to the firstapproximation, but, the fact that even the best performing correlations end up under-predicting the experimental data implies that there needs a specific correlation formicrogravity data.

Fang et al., in a separate study [42], reported the development of a newcorrelation specifically for microgravity two phase flow which could predict theexperimental data better than all existing correlations:

lo2 = Y2x0.87 + (1-x0.626)0.54[1 + 2x1.823(Y2 - 1) + 47.74x1.4]

where lo2 is defined according to convention.

SUMMARY

In comparison with the single phase flow applications being presently utilized,two phase flows have many advantages which make them desirable for use in bothmicrogravity as well as hyper-gravity environments. However, the current level ofknowledge is not sufficient to reliably design a two phase loop system.

There is consensus that there are three major flow regimes in microgravity:bubbly, slug and annular. However, there is considerable confusion regarding theboundaries between the different flow regimes. Various attempts - extrapolating 1-g flowregime maps to microgravity, classification using semi-empirical void fraction relations,theoretical force balance analyses - at defining the flow regime boundaries have yieldeddifferent transition criteria. Among those available, Duklers flow regime map ispreferable. The dimensionless analysis using the liquid Suratman number - while giving

15


16/18

no reasons for the dramatic change in the behaviour of the two phase mixture at Su =106, fits most of the data with reasonable accuracy.

There has been some understanding gained about bubble dynamics in amicrogravity environment. The shape of the bubble is nearly spherical, since the

distortion effect due to buoyancy is eliminated. With increasing inlet velocities, theaverage bubble size decreases. This may be attributed to greater heat loss due toconvection to the ambient flow. If the Reynolds number of the flow is very high, thebubble size and shape resemble that observed in normal gravity conditions, implyingthat gravity effects are no longer influential when inertia dominates. The bubble does notdepart from its nucleation site, unless it is forced by the inertial effects of the flow. Thelack of buoyancy - which on earth would provide a lift force to the bubble - makes thebubble roll on the surface of the heater, while it grows in size due to heating from theheater or coalescence with other bubbles, until the velocity and shear gradients in theflow distort its spherical shape and lift it into the center of the flow. Once the bubblereaches the center of the flow, i.e., the shear force on the bubble surface is uniform,

surface tension forces the bubble to the shape of a sphere again. The heat flux at theheater surface and the inlet flow velocity influence bubble growth and frequency ofbubble nucleation and departure. A greater understanding of the underlying mechanismwould be helpful in clearing up the confusion regarding microgravity heat transfer.

The study of microgravity heat transfer has been constrained by the relativelysmall amount of experimental data available and the lack of standardized testapparatus. On the basis of available data, the heat transfer has been found to bestrongly dependent on the flow regime, with the heat transfer for annular flows beingpractically independent of gravity. This may be explained by the dependence offrequency of bubble departure and nucleation site density on the mass flow rates and

heat fluxes applied.

The importance of having a thorough knowledge of the critical heat flux cannotbe over-emphasized, since it is the surest way of destroying equipment. The interfacialliftoff model proposed by Galloway and Mudawar and extended by Zhang et al. gives areasonably accurate prediction of the experimental data. The model has been found towork equally well for sub-cooled flows, with minor modifications.

The pressure drop, in a microgravity environment, has been found to be stronglydependent on the tube diameter and the void fraction. Although a number of empiricaland semi-empirical correlations have been proposed to determine the pressure drop,

the difficulty of obtaining void fraction data has resulted in an incomplete understandingof this topic. A recent comparison of the existing correlations has revealed that theMcAdams and the Muller-Steinhagen and Heck correlations performed best. Thepressure drop was also found to be independent of the orientation.

Further studies, with standardized test methods, is required to clear up the manyhazy points in our present understanding of microgravity heat transfer, before anypractical applications can be realized. One way of getting around this scientific gestation

16


17/18

period is to ramp up the allocation of energy to pumping appliances, since the effects ofgravity, be it micro or hyper, greatly diminish when inertia is dominant.

ACKNOWLEDGEMENT

I would like to gratefully acknowledge the assistance rendered by Prof. HaruhikoOhta in sending me several figures from his research.

REFERENCES

1. A.E.Dukler,J.A.Fabre,J.B.Mcquillen,R.Vernon,1988,Gasliquid?lowatmicrogravityconditions:?lowpatternsandtheirtransitions.Int.J.MultiphaseFlowVol.14,389400.

2. MarcDhainaut,2002,Literaturestudyonobservationsandexperimentsoncoalescenceandbreakupofbubblesanddrops.SINTEFReportSTF24A02531

3. A.M.Kamp,A.K.Chesters,C.Colin,J.Fabre,2001,Bubblecoalescenceinturbulent?lows:Amechanisticmodelforturbulenceinducedcoalescenceappliedtomicrogravitybubbly?low.Int.J.MultiphaseFlowVol.27,13631396.

4. YehudaTaitel,LarryWhite,1996,Theroleofsurfacetensioninmicrogravityslug?low.Chem.Engg.Sci.Vol.51,695700.

5. EastmanR.E.,FeldmanisC.J.,HaskinW.L.,WeaverK.L.,1984,Twophasethermaltransportforspacecraft.TechnicalReportNo.AFWALTR843028.

6. J.Weisman,S.Y.Kang,1981,Flowpatterntransitionsinverticalandupwardlyinclinedlines.Int.J.MultiphaseFlowVol.7,271291.

7. S.B.R.Karri,V.K.Mathur,1988,Twophase?lowpatternmappredictionsundermicrogravity.AIChEVol.34,137139.

8. L.Zhao,K.S.Rezkallah,1995,Pressuredropingasliquid?lowundermicrogravityconditons.Int.J.MultiphaseFlow.Vol.21,837849.

9. L.Zhao,K.S.Rezkallah,1993,Gasliquid?lowpatternsatmicrogravityconditions.Int.J.MultiphaseFlow.Vol.19,751763.

10. R.M.MacGillivray,K.S.Gabriel,2003,Astudyofannular?low?ilmcharacteristicsinmicrogravityandhypergravityconditions.ActaAstronautica.Vol.53,289297.11. K.S.Rezkallah,1996,Webernumberbased?lowpatternmapsforliquidgas?lowsat

microgravity.Int.J.MultiphaseFlow.Vol.22,12651270.12.M.Parang,D.Chao,1998,Twophase?lowmappingandtransitionundermicrogravity

conditions,36thAIAAAerospaceSciencesMeetingandExhibit.13.W.S.Bousman,1995,Studiesoftwophasegasliquid?lowinmicrogravity.NASAReportNo.

195434(N9524906).14. S.S.Jayawardena,V.Balakotaiah,L.C.Witte,1997,Flowpatterntransitionmapsfor

microgravitytwophase?low.AIChEVol.43,16371640.15. J.F.Zhao,W.R.Hu,2000,Slugtoannular?lowtransitionofmicrogravitytwophase?low.Int.

J.MultiphaseFlow.Vol.26,12951304.16.NilavaSen,2010,Twophaseslugtoannular?lowpatterntransitioninmicrogravity.Acta

Astronautica.Vol.66,13731377.17. L.Valota,C.Kurwitz,A.Shephard,F.Best,2007,Microgravity?lowregimeandanalysis.Int.J.

MultiphaseFlow.Vol.33,11721185.18.M.G.Cooper,K.Mori,C.R.Stone,1983,Behaviourofvaporbubblesgrowingatawallwith

forced?low.Int.J.HeatandMassTransfer.Vol.26,14891503.19. T.C.Wang,T.J.Snyder,J.N.Chung,1996,Experimentalexaminationofforcedconvection

subcoolednucleateboilinganditsapplicationinmicrogravity.J.ofHeatTransfer.Vol.118,237241.

17


18/18

20. YueMa,J.N.Chung,2001,Astudyofbubbledynamicsinreducedgravityforcedconvectionboiling.Int.J.ofHeatandMassTransfer.Vol.44,399415.

21.D.Serret,D.Brutin,O.Rahli,L.Tadrist,2010,Convectiveboilingbetween2Dplates:Microgravityin?luenceonbubblegrowthanddetachment.MicrogravitySci.Technol.Vol.22,377385.

22.N.N.Clarke,K.S.Rezkallah,2001,Astudyofdriftvelocityinbubblytwophase?lowunder

microgravityconditions.Int.J.ofMultiphaseFlow.Vol.27,15331554.23.M.Misawa,S.Anghaie,1991,Zerogravityvoidfractionandpressuredropinaboiling

channel.AIChESymp.Ser.87,226235.24.M.Kawaji,C.J.Westbye,B.N.Antar,1991,Microgravityexperimentsontwophase?lowand

heattransferduringquenchingofatubeand?illingofavessel.AIChESymp.Ser.87,236243.

25. T.R.Reinarts,F.R.Best,W.S.Hill,1992,De?initionofcondensationtwophase?lowbehavioursforspacecraftdesign.AIPConferenceProc.No.246,Vol.1,12161225.

26.M.Saito,N.Yamaoka,K.Miyazaki,M.Kinoshita,Y.Abe,1994,Boilingtwophase?lowundermicrogravity.NuclearEnggandDesign,Vol.146,451461.

27.H.Ohta,2003,Microgravityheattransferin?lowboiling,AdvancesinHeatTransfer,Vol.37,176.

28. R.W.Rite,K.S.Rezkallah,1997,Localandmeanheattransfercoef?icientsinbubblyandslug

?lowsundermicrogravityconditions.Int.J.ofMultiphaseFlow.Vol.23,3754.29. R.K.Lui,M.Kawaji,T.Ogushi,1994,Anexperimentalinvestigationofsubcooled?lowboiling

heattransferundermicrogravityconditions.10thInternationalHeatTransferConference,BrightonVol.7,497502.

30. G.P.Celata,G.Zummo,2008,Flowboilinginmicrogravity.EBECEM20081EncontroBrasileirosobreEbulio,CondensaoeEscoamentoMultifsicoLquidoGs.

31. C.Baltis,G.P.Celata,M.Cumo,L.Saraceno,G.Zummo,2012,Gravityin?luenceonheattransferratein?lowboiling.MicrogravitySci.Technol.Vol.24,203213.

32. YueMa,J.N.Chung,2001,Anexperimentalstudyofcriticalheat?luxinmicrogravityforcedconvectionboiling.Int.J.ofMultiphaseFlow.Vol.27,17531767.

33.H.Zhang,I.Mudawar,M.M.Hasan,2002,Experimentalassessmentoftheeffectsofbodyforce,surfacetensionforceandinertiaon?lowboilingCHF.Int.J.ofHeatandMassTransfer.Vol.45,40794095.

34. J.E.Galloway,I.Mudawar,1993,CHFmechanismin?lowboilingfromashortheatedwallpart2.TheoreticalCHFmodel.Int.J.ofHeatandMassTransfer.Vol.36,25272540.

35.H.Zhang,I.Mudawar,M.M.Hasan,2002,Experimentalandtheoreticalstudyoforientationeffectson?lowboilingCHF.Int.J.ofHeatandMassTransfer.Vol.45,44634477.

36.H.Zhang,I.Mudawar,M.M.Hasan,2005,FlowboilingCHFinmicrogravity.Int.J.ofHeatandMassTransfer.Vol.48,31073118.

37.H.Zhang,I.Mudawar,M.M.Hasan,2007,CHFmodelforsubcooled?lowboilinginEarthgravityandmicrogravity.Int.J.ofHeatandMassTransfer.Vol.50,40394051.

38. I.Chen,R.Downing,E.Keshock,M.Alsharif,1991,Measurementsandcorrelationoftwophasepressuredropundermicrogravityconditions.J.Thermophys.Vol.5,514523.

39. C.Colin,J.Fabre,1995,Gasliquidpipe?lowundermicrogravityconditions:in?luenceoftubediameteron?lowpatternsandpressuredrops.Adv.SpaceRes.Vol.16,137142.

40. J.F.Zhao,J.C.Xie,H.Lin,W.R.Hu,A.V.Ivanov,A.Yu.Belyaev,2001,Experimentalstudiesontwophase?lowpatternsaboardtheMirspacestation.Int.J.ofMultiphaseFlow.Vol.27,19311944.

41. XiandeFang,HonggangZhang,YuXu,XianghuiSu,2012,Evaluationofusingtwophasefrictionaldropcorrelationsfornormalgravitytoreducedgravityandmicrogravity.Adv.SpaceRes.Vol.49,351364.

42. XiandeFang,YuXu,2013,Correlationsfortwophasefrictionpressuredropundermicrogravity.Int.J.ofHeatandMassTransfer.Vol.56,594605.

18

Documents

Flow boiling in microgravity - a review