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Strojarstvo55 (1) 45-56 (2013) M. PANAO et. al., Intelligent thermal management for full 47

Through the advanced statistical tool of the finitemixture of probability density functions (pdf), drop sizeand axial velocity distributions are involved in the physical interpretation of the flow, instead of limiting itto first and second order distribution moments. Eachgroup of droplets with similar size characteristics has been modelled by lognormal distributions, and normaldistributions relative to drop axial velocity.Furthermore, droplet characteristics are correlated withthe heat transfer rate for several operating conditionsthat maintain the surface temperature in the steady-stateat 125C, which is the operating value recommended for

IGBT-based power electronic devices. The effect of thetime between consecutive injections is analysed.Relative to the spray operating mode, most research

works reported do not take into account an activecontrol of the cooling process required for an intelligentthermal management during periods of transient heatloads. The active control of heat transfer can beinterpreted as a spatial control [4], or temporal controlover the flow rate using an intermittent spray [5, 6].Considering the point of view of developing two-phasecooling technologies that take benefit from phase-change, intermittent spray cooling is compared with thecurrent proposals based on continuous sprays. While thecorrelation between droplets characteristics and heattransfer only consider the spray produced by the impactof 3 jets, when comparing the benefit from phase-change, the sprays produced by the impact of 2 and 4 jets are also taken into account. The synthesis of thescattered information on this subject provides theguidelines for research trends in the development ofintelligent thermal management technology.

2. Methodology

2.1. Experimental setup

The characterized spray issues from a multijetimpingement atomizer with N j = 3 impinging jetsmaking an impact angle (2 ) between them of 90 andequally spaced in terms of azimuthal angle. The jets areconsidered to have the same diameterd j = 400m as thehole in the atomizer. The liquid supply line works in aclosed circuit and a pressure regulation valve allowscontrolling its value in the monorail coupled with theinjector. This pressure has been set to the same valueused in the heat transfer experiments previouslyreported [7], corresponding to 1.6 bar. For this pressuredifferential at the atomizer exit, a nominal volumetricflow rate of 3.33 ml/s is obtained with the injector valvefully open, and it varies depending on the duty cycle( , see Fig. 1) as

. Each jet velocity is8.8m/s. The liquid is methanol, which is a dielectricfluid with a density ( ) of 781.6 kg/m3, dynamicviscosity ( ) of 5.24910-4 kg/(m/s), surface tension ()of 21.92 mN/m at 30C, thermal conductivity (k f ) of0.2033 W/m/K and a latent heat of vaporization (h fg) of1168 kJ/kg.

Heat transfer experiments previously reportedconsidered the effect of the non-injection time betweenconsecutive injections as it is illustrated inFig. 1 [7]. These non-injection times have been set to10, 20 and 40 ms while keeping a constant duty cycle(DC, see definition in Fig. 1, where f inj is the injectionfrequency and t inj the duration of injection). Thus, adecrease of this period means that the amount of massinjected in the largest cycle is actually being distributed into multiple injections (seeillustration in the lower-left part of Fig. 1).

Nu - Nusselt number / Nusseltov broj Subscripts/Indeksi

PEEM- Power Electronic and Electrical

Machines / Energetska elektronika ielektrini ureaji

c - critical /kritino

pdf - probability density function /

funkcija gustoe vjerojatnostid - droplet / kapljice

- dissipated heat / rasipanje topline,W m-2 D -

diameter / promjer

- sensible heat / osjetna toplina, W m-2 inj - injected / ubrizgavanje- injection cycle volume flow rate /

ciklus ubrizgavanja volumena protoka, m3s-1

j - jet / mlaz

T b- boiling temperature / temperatura

vrenja, K U - axial velocity / aksijalna brzina

T f- coolant temperature / temperatura

rashladne tvari, KTTL -

Transistor-Transistor Logic /Tranzistor-tranzistor logika

U j - jet velocity / brzina mlaza, m s-1

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48 M. PANAO et. al., Intelligent thermal management for full Strojarstvo55 (1) 45-56 (2013)

The heat transfer results reported in Panoet al. [7]will be used in this work in order to correlate with thespray droplets characteristics. These (size and axialvelocity of droplets) have been measured with a Phase-Doppler Interferometer collecting the light dispersed by

droplets at a scattering angle of 74, which correspondsto the Brewster angle for methanol, with the purpose ofminimizing the reflected light with a parallel polarization. The beam spacing is 60 mm and bothtransmitting and receiving lens have a 500 mm focallength, thus, the maximum measurable diameter is350m.

2.2. Statistical method for spray characterization

The data on the size and axial velocity of droplets inthis work is statistically described by discrete probability density distributions. Usually, thesedistributions are further used in a statistical analysis,which is based on its moments,e.g. mean quantities orstandard deviation. However, it has been argued in a previous work that such approach, although correct,gives only a partial and limited knowledge of themeasured distribution [8]. On the other hand, for thedevelopment of numerical models, it is an advantage todescribe such distributions by mathematical pdffunctions (e.g. Lognormal) or empirical models (e.g. Nukyiama-Tanasawa, Rosin-Ramler, Weibull, for acomprehensive review see Babinsky and Sojka [9]).However, probability distributions describing sprays are

often multimodal, or presented with heterogeneities.Thus, when the actual distribution is approximated to aunimodal mathematical function, with its characteristic parameters, and the latter are used to evaluategeometric, operating or environmental parametriceffects on the spray formation and development, theanalysis becomes limited. In order to overcome theselimitations, in this work, discrete probabilitydistributions characterizing the spray have beenmathematically modelled using the known statistical

tool of finite mixtures of probability density functions.This tool consists in identifying the numberK of groupsof droplets with similar characteristics and empiricallyfitting the discrete probability distribution to a linearcombination of weighted probability density functions

as(1)

where wi is the weight and are the characteristic parameters of the mathematical probability densityfunction. In the experimental characterization reportedhere, for each group of droplets, the size has beenmodelled by a Lognormal pdf , anddrop axial velocity by a Normal pdfThe fitting procedure followed a Bayesian approach previously applied to sprays by Panoet al. [8] and

Pano and Radu [10]. Therefore, instead of usingcharacteristic means values, which are limited fordescribing multimodal drop size and velocitydistributions, the parameters of the finite mixture areused instead. The same formulation for a finite mixturegiven in eq. (1) can also be used with cumulativedistribution functions (Fmix or Fi). In terms of flowanalysis, this ultimately means that the entiredistribution is being considered, and not just itsmoments. The best finite mixture is that whichmaximizes the Marginal Likelihood (ML) or theminimum K above which ML stabilizes [10]. Theresulting finite mixtures obtained have been subjected toa chi-squared test with a 99.9% of confidence intervaland the hypothesis that the mathematical curve fits datahas been accepted in all cases.

re 1. Illustration of the spray injection cycle and description of the experimental conditions considered for studyingthe effect of the spray intermittency on heat transfer.

a 1. Prikaz ciklusa ubrizgavanja rasprivanjem i opis eksperimentalnih uvjeta koji su uzeti u obzir u prouavanjuuinka isprekidanog rasprivanja na prijelaz topline.

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2.3. Quantifying the benefit from phase-change

The main advantage of a two-phase cooling is to benefitfrom phase-change. If we assume a subcooling

other than zero, when the spray impacts

onto the heated surface, part (and ideally all) of theinjected liquid deposits on the surface and itstemperature increases up to the liquids boiling point atambient isobaric conditions, through the removal ofsensible heat from the surface.Afterwards, a large portion of heat is removed by phase-change through evaporation by mass diffusion at theliquid-vapour interface in a non-saturated environmentand non-boiling regime; or else, in a nucleate boilingregime, with the formation of bubbles at the solid-liquidinterface. Thus, heat transfer performance depends onliquid film formation and dynamics, as well as thecomplex flow generated by nucleate boiling.Additionally, the hydrodynamics associated withmultiple drop impacts [11], or the formation ofsecondary nuclei through vapour entrainment from theliquid-vapour interface [12], have their important role inheat transfer processes. Namely, Zhaoet al. [13] havevalidated a model which allows for the assessment ofthe relative importance on heat transfer between:i)drop-wall impaction;ii) film-wall convection;iii) heatdissipated to the environment;iv) and bubble boiling;concluding that for the range of heat fluxes expected todissipate in IGBT's (200-300 W/cm2), the maininfluences are due to drop impaction and bubble boiling,

expressing a strong relation between both hydrodynamicmechanisms and phase-change. However, the researchquestion is how to quantify how much benefit or notdoes a system take from phase-change.

Given the above description, in order to quantify the benefit associated with phase-change, we first considerthat the heat dissipated by the spray ( ) is removed by the part of liquid which accumulates on the surfacein the form of a liquid film , where is nullfor no deposition, or 1 for a full deposition. Also,thermodynamically, unless the subcooling degreeis zero, the accumulated liquid film exchanges sensibleheat to increase its temperature up to the boiling valuefor local ambient conditions, while the remaining heat isexchanged through a non-boiling, or boiling phase-change. This can be expressed as

(2)

where is the volumetric flow rate injected,, c p andh fg are the liquid's density, specific heat and latent heatof vaporization, respectively. Parameter is our proposal for quantifying the "benefit from phase-change " between different spray cooling systems. Usingthis parameter for comparison purposes implies takinginto account not only different cooling liquids, but also

different relations between heat transfer and sprayimpact hydrodynamics.

In order to explain this, eq. (2) is solved for , becoming a function of two terms:i) a normalized heatflux ; ii) and the Jakob

number Ja = as

Ja (3)

Relative to the Jakob number (Ja), a liquid with asmaller Ja is more likely to benefit from phase-change,than one with a higher Ja, although one can alwaysreduce Ja by decreasing the subcooling degree. Thenormalized heat flux term stands for implicationsof the relation between heat transfer and the liquidaccumulated on the surface for cooling purposes,relative to the benefit from the phase-change a thermal

management system might retrieve. It can be easilyunderstood that: if = 0 there is no benefit from phase-change; while = 1 implies full benefit. Moreover, inorder to understand the theoretical limits of , weconsider the general definition of cooling efficiency

(4)

which could be included in Eq. (3) resulting in

(5)

If one considers the several physical constraintsassociated with the parameters involved, relative to themost unknown variable, which is the fraction of liquidinjected that accumulates on the surface,

, it yields as a solution thefollowing cases:

1. if = 0 and Ja = 0, the partial deposition ofliquid may assume any of its values within its physical limits;

2. if = 1 and Ja 0, full deposition is expectedwith = 1;

3. if Ja is compared with the ratio * = /(1-),the partial deposition ofliquid is expected tolie between the value of the cooling efficiency and a maximum of1 if Ja *, or (1+Ja)/if Ja > * .

In the first case, when tends to 0% , and Ja is verysmall, the latent heat may be high relative to thesensible heat, but there is little or no benefit from phase-change , corresponding to a spray impact on anon-heated surface. In the second case, obviously, anefficiency of 100% could only mean total deposition ofthe liquid injected and full benefit from phase-change

. The third case sets a physical minimum of

.

.

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The standard deviation 2,U varies only 1.8% between cases, and the variability of 2,U is alsomoderate, about 6.2%. In fact, the maximum variation between operating conditions is approximately 47% ofaverage standard deviation of all operating conditions,

indicating that the effect of the spray intermittency ofthe spray characteristics is relatively low. Nonetheless,if this component is correlated with the duty cycle (DC),one observes a systematic pattern where the axialvelocity distribution shifts to lower characteristic valuesfor every non-injection time condition (see Fig. 5). Namely, for lower DCs, the effect of injection splittingis slightly more pronounced.

Relative to droplet size, given the presence of threegroups of droplets, a weighted characteristic meandiameter is considered and defined as

, and when plotted against DC,unlike droplets axial velocity, the absence of correlation becomes evident (see Fig. 6).

Figure 5. Variation of the second group of the axial velocitydistribution ( 2,U ) with the duty cycle (DC)

Slika 5. Promjene distribucije aksijalne brzine u drugojskupini ( 2,U ) s radnim ciklusom (DC)

Nonetheless, the magnitude of the measured value iswithin the range expected for multijet impingementsprays formed from turbulent liquid sheets, since thehydrodynamics of the atomization process has been

shown to be similar regardless the number of impinging jets [14]. For N j = 2 jets, Anderson et al. [15] have provided an empirical correlation for the arithmeticmean diameter as ,where We j is the Weber number of the jet (= U j2d j/)and . Fig. 6 includesthe value obtained for the geometrical configuration ofthe atomizers used in this work, confirming thesimilarity in the order of magnitude.

Figure 6. Weighted characteristic mean diameter of droplets( K,D) as a function of DC. The dashed linecorresponds to the estimation of the arithmetic

mean diameter for sprays produced by turbulentsheets formed from the impact of two jetsaccording to Andersonet al. [15]

Slika 6. Teinska karakteristika prosjenog promjerakapljica ( K,D) kao funkcija DC. Isprekidana linija

predstavlja procjenu aritmetike sredine promjer aza rasprivae koje proizvode turbulentne ploeformirane utjecajem dva mlaza prema Andersonetal. [15]

3.2. Local influence of spray characteristics onliquid deposition and heat transfer

Spray impingement heat transfer events depend on thedeposition of the liquid injected on the heated surfaceand the ability to control it. In previously reportedresults, if spray impaction is unavoidable, the best heattransfer efficiency for cooling purposes is achieved if athin liquid film remains present on the heated surface[7]. Consequently, the highest heat transfer efficiencieswere obtained with short time intervals betweenconsecutive injection cycles (10 ms).

On the other hand, in terms of predicting theoutcome of spray impact, the criteria in the model ofBai et al. [16] are used to discern between the basic

hydrodynamic mechanisms of:i) Deposition:a. stick (Wed 2) and b. spread (20 < Wed We c = 1320 Lad -0.183) which

contribute to the formation of a liquid film;ii) and Secondary Atomization:

c. rebound (2 < Wed 20) ord. splash (Wed > 1320 Lad -0.183), where Wed is the

Weber number of droplets,Wed = K,U 2 K,D/, and Lad is the Laplacenumber (Lad = K,D/ f 2, where f is the fluiddynamic viscosity).

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These criteria have been applied to drop size andvelocity data, and the percentage of drops in eachmechanism has been estimated. Fig. 7 shows the effectof the duty cycle (DC) on the efficiency of the heattransfer process (below) and the percentage of droplets

in the spray expected to deposit on the impingingsurface (above). According to the criteria of Baiet al. [16], slightly more than half of the spray droplets areexpected to deposit on the surface, and a trend forslightly increasing this fraction or percentage isobserved as DC approaches the condition of acontinuous spray (DC = 100%).

The evolution of the deposition percentage with DC,observed in Fig. 7, is coherent with the observed factthat a higher DC implies a larger mass flux injected,leading to thicker liquid films and jeopardization of heattransfer [7]. However, while it is evident that a shortertime between consecutive injections improves the heattransfer efficiency, no such trend is observed relative tothe fraction of droplets expected to deposit on thesurface.

Figure 7. Effect of the duty cycle (DC) on the efficiency andexpected deposited fraction of droplets for non-injection times of 10, 20 and 40 ms

Slika 7. Utjecaj radnog ciklusa (DC)na uinkovitost ioekivanu pohranu dijela kapljica u vremenu bezubrizgavanja od 10, 20 i 40 ms

On the other hand, the behavioural pattern of the axialvelocity with DC, shown in Fig. 5, is similar to themonotonic decrease observed for the heat transferefficiency in Fig. 7 (bottom). This would be consistentwith the fact that impinging droplets are likely to piercethe liquid film, allowing cooler liquid to reach thesurface more efficiently, particularly in the cases ofthinner liquid films, thus enhancing heat transfer. Theseresults suggest that not only the axial velocity might bea determinant parameter for heat transfer [17], but more

so the relation between droplet velocity and a controlledliquid film thickness.

Using the heat transfer data with that of the spraycharacteristics, a correlation is sought. However, the purpose is not to provide a new empirical correlation per se , but rather to physically interpret the valueobtained for its constant parameters. In order todistinguish the effects of drop size and velocity, twodimensionless numbers have been used, the Laplace Lad = Red 2/Wed ~ g(D) and Capillary Cad = Wed /Red ~ g(U)numbers. The Nusselt number is defined as Nu =hsc K,D /k f , with hsc as the heat transfer coefficient, K,D the weighted characteristic mean diameter andk f theliquid thermal conductivity. In Fig. 8, it is observed howheat transfer is higher for the most efficient operatingconditions , while increasing the time between consecutive injection cycles leads to lower heattransfer rates. This evidences the importance of theability to control the presence of a thin liquid film forspray cooling.

Figure 8. Variation of Nu as a function of the duty cycle(DC) for different non-injection times betweenconsecutive cycles

Slika 8. Promjena Nu kao funkcija radnog ciklusa (DC) zarazliita vremena bez ubrizgavanja izmeuuzastopnih ciklusa

The Lad and Cad numbers have also used weightedcharacteristic mean parameters ( K,D and K,U ) in theircalculation. The empirical correlation has the typicalform of

(6)

wherea , b and c are the correlation constants. Althoughheat transfer correlations usually use the Prandtl number(Pr), relating the kinematic and thermal diffusivities, thefluid is the same in every experiment, as are theenvironmental conditions. Therefore, the effect of Prwould be constant and, thus, included in constanta .

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Using a direct least square method,b and c areestimated to be negative (see Fig. 9-top), suggesting that by increasing the size, since Lad >> 1 b < 0, heattransfer is jeopardized, while by increasing the axialvelocity of impinging droplets, since Cad < 1 c < 0,heat transfer is improved. Usually, there is a positivecorrelation between droplet size and velocity, i.e. largerdroplets are less prone to interact with the surroundingenvironment, and thus, are faster than smaller droplets.Therefore, the constant parameters in this correlationindicate a competition between these two effects.However, Fig. 9 (bottom) shows how the effect exerted by the dimensionless parameter Cad , associated with theaxial velocity, is more influential relative to the dropsize associated with Lad .

An additional point is that faster droplets havegreater impact energy and their likely outcome is not todeposit on the surface for cooling purposes, buteventually to trigger secondary atomization mechanismsand generate secondary droplets. In this case, part of theliquid is not in contact with the surface, but eventuallydeposits at a later time, and since the impact energy ofsecondary droplets is typically much lower, these areexpected to deposit and remove heat by phase-change.

Figure 9. Comparison between Nu obtained experimentallyand through an empirical correlation (top); andinfluence of dimensionless numbers Cad and Lad on the Nusselt number (bottom)

Slika 9. Usporedba izmeu Nu dobivene eksperimentalnokroz empirijske korelacije (gore); i utjecaj

bezdimenzijskih brojeva Cad and Lad na Nusseltov broj (dolje)

3.3. Toward intelligent thermal management

In order to have an intelligent thermal management, it isimportant to devise a strategy that allows an activecontrol over the cooling process. Pavlovaet al. [4] haveexplored the flapping of a spray produced by synthetic jets, using piezoelectric actuators, to perform the activecontrol of the spray density upon its impaction, thus,enabling the control of heat transfer in the non-boilingregime. Pano and Moreira [5] proposed an IntermittentSpray Cooling (ISC) strategy, where the parametercontrolling heat transfer has been identified as the DutyCycle ( ), through which onemay control the time and interaction betweenconsecutive injections. Consequently, a greater or lesserdegree of saturation near the liquid-vapour interface can be obtained, influencing the vaporization rate andeventually extracting a greater benefit from phase-change cooling. However, the same DC can be obtainedwith different matches between frequency and durationof injection, therefore, the question remains as to whichis the best and most efficient choice. In Panoet al. [7],the degree of interaction between multiple consecutiveinjection cycles has been analyzed by varying thefrequency of injection, or the time interval between theend of an injection and the start of the next one,considering also its implications for the efficiency of thecooling process. It has been observed that the highestfrequency possible (within the constructive constraintsof the electromechanical valve) should be chosen formaximizing heat transfer.

The way in which the cooling liquid is directlyspread throughout the heated surface implies a carefulchoice of the atomization strategy. A tailored spraywould break into small, well dispersed, droplets, which,upon impact, are more likely to deposit on the surface,depending on the hydrodynamic and heat transferimpinging mechanisms [11]. In Panoet al. [14], astrategy has been studied which produces a spraythrough the single-point impact of multiple cylindrical

jets, thus referred as multijet impingement atomization.In this kind of atomization, the collision between two ormore jets generates a liquid sheet, which destabilizeswhile developing due to the interaction between inertialand surface tension forces with the surrounding air,disintegrating into droplets at the liquid-air boundary.For the characterization of the spray reported in [14], its potential applicability to microprocessors cooling has been assessed in Panoet al. [6]. Moreover, the abilityof using the spray intermittency for controlling surfacetemperature has been demonstrated in Panoet al. [18],although within the microprocessor context where theheat fluxes are much lower, but one should not expect a

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significant difference if applied to power electronicdevices.

Furthermore, it has already been mentioned thattwo-phase convective cooling (such as spray cooling)has been claimed as the best choice for developing a

thermal management system for cooling IGBT powermodules used in power electronics, because it boosts power density while keeping the volume/weight/cost aslow as possible. The justification for this claim lies inthe benefit of removing heat through phase-change.Therefore, how does intermittent spray cooling (whichmay also work in a continuous mode) compare withsystems based on continuous sprays reported in theliterature?

The -parameter is used in this comparison becauseit quantifies the benefit of phase-change and allows forcomparison between different cooling configurations,using different liquids and atomization strategies. A preliminary analysis of the results reported in theliterature shows that some dissipated heat fluxes may bevery high, but it does not mean that such an outcome isrelated to the benefit of phase-change. Namely, whenthe criterion defined in case 3 of the solution presentedin section 2.3 is applied, some results evidence thatthose high dissipated heat fluxes are not the result of phase-change cooling, but of the larger amount ofsensible heat removed at a given operating condition. Ifthe aforementioned criterion is expressed as

, the first case indicates benefitfrom phase-change, and thus a dominant two-phaseconvective cooling, while the second case indicates that phase-change is mitigated and single-phase cooling becomes the dominant heat transfer mechanism (seeFig. 10).

It is noteworthy from Fig. 10 how most experienceswhich lead to the mitigation of phase-change have wateras the cooling liquid, except for two conditions in thework of Chen et al. [19], which differ from theremainder by the larger than average size of the spraydroplets. This suggests that dielectric fluids are moreappropriate for the direct cooling of power electronicdevices.

Figure 10. Comparison between the dissipated heat flux andthe criterion

Slika 10. Usporedba izmeu rasipanja toplinskog toka i

kriterija

Figure 11. Comparison between the dissipated heat flux andthe -parameter

Slika 11. Usporedba izmeu rasipanja toplinskog toka i parametra

If we now consider only the cases which benefit from phase change and compare the amount ofdissipated heat flux with the -parameter (see Fig. 11),assuming the worst scenario for phase-change coolingwhere all the liquid injected is accumulated at thesurface, = 1 (in reality, if < 1, would increase),several considerations can be made:

a higher heat dissipation rate does not imply alarger benefit from phase-change;

except for a slight improvement in Mudawaret al.[24], in continuous spray cooling, variations in theflow rate [19, 20] do not produce any significanteffect on the benefit of phase-change. Namely, it issuggested that in intermittent spray cooling,changing the Duty Cycle, and, consequently,changing the degree of interaction between

consecutive cycles, allows for the same heatdissipation ability, but increasing the benefitextracted from phase-change. Namely, it issuggested that a lower DC, implying more time between consecutive cycles relative to the injectiontime, allows a less saturated environment at theliquid-vapour interface and promotes heatexchanges through the latent heat of vaporization.

4. Concluding remarks

The argument in this paper is that thermal management plays a crucial role in the development of the powertrainin electric vehicles. Namely, the energy demands

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occurring during power peaks imply that losses in power electronic devices are likely to vary within thevehicle's driving cycle. Therefore, an intelligent thermalmanagement able to efficiently respond to these power peaks is advantageous and the investigation of an

intermittent multijet impingement spray for directcooling purposes constitutes the main motivation forthis work. A local analysis is made on the correlation between the characteristics of a multijet impingementspray and the heat transfer that keeps the surfacetemperature in a steady-state condition at 125C. Thespray is characterized through a statistical analysis usingfinite mixtures of weighted Lognormal distributions fordescribing the polydispersed sizes of droplets andnormal distributions for describing their axial velocitycomponent (perpendicular to an impinging surface). Theadvantage of using this more advanced statistical tool isthat one considers the entire distribution in the analysis,instead of its moments alone.

Results for the spray characteristics evidence: the presence of three groups of droplets

characterizing the spray in every intermittentoperating condition. However, the groups withmedium and large characteristic sizes aredominant relative to the group of smallerdroplets;

droplets size polydispersion expressed by thestandard deviation of the log-normal is wellcorrelated with the characteristic size as

(R 2 = 0.996); droplets axial velocity is mainly constituted bya group around 86% of the jet velocity

(8.8m/s), and does not significantly vary withthe duty cycle (DC).

The characteristics of droplets have been measuredfor the same operating conditions of previously reportedheat transfer experiments, in order to evaluate theircorrelation, as well as the expected outcome of impact.Results evidence that multiple injection pulses withshorter time intervals between consecutive cyclesinduce a greater importance to the relation betweendroplets axial velocity and the control of the liquid filmthickness for heat transfer enhancement.

Moreover, if the advantage of spray cooling is to benefit from phase-change, it is important to devise a parameter which allows the evaluation of such benefitand enables the comparison of different sprayconfigurations, liquids and hydrodynamics on sprayimpaction, including the implications of the degree ofliquid accumulation on the surface. This -parameterhas been devised and has been found to depend on thecooling efficiency , accumulated mass flux and theJakob dimensionless number, which relates the heatassociated with the subcooling degree with the latentheat.

Given the body of experimental work reported in theliterature, a comparison is made between those studiesaddressing the issue of high heat fluxes in powerelectronics. According to the analysis of , not all benefit from phase-change, and of those that benefit,

only the intermittent spray cooling strategy has theability to control that benefit through the duty cycle. Namely, with a lower degree of interaction betweenconsecutive injection cycles, the system benefits morefrom phase-change cooling, thereby demonstrating the potential use of intermittent spray cooling fordeveloping an intelligent thermal management for power electronics devices in full electrical vehicles.

Acknowledgements

The author would like to acknowledge Fundao para a

Cincia e Tecnologia for supporting his researchthrough project MUST (PTDC/EME-MFE/099040/2008) and Miguel Oliveira Pano with a postdoc fellowship SFRH/BPD/45170/2008.

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