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Applied Thermal Engineering

journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Modelling of liquid nitrogen spray cooling in an electronic equipment cabinunder low pressure

Chao Wang, Yu Song, Peixue Jiang⁎

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Beijing Key Laboratory for CO2 Utilization and Reduction Technology, Department ofEnergy and Power Engineering, Tsinghua University, Beijing 100084, China

H I G H L I G H T S

• A strategy was proposed for thethermal control of the electronicequipment cabin.

• Liquid nitrogen droplet flash eva-poration under low pressure is ad-dressed.

• Switching frequency of spray nozzlesis influenced by temperature controllimits.

• Interaction between pressure andtemperature during spray cooling waspresented.

• The study can help to ascertain op-timum operational conditions ofspraying cooling.

G R A P H I C A L A B S T R A C T

A R T I C L E I N F O

Keywords:SpacecraftSpray coolingElectronic equipmentThermal management

A B S T R A C T

Timely and effective cooling is essential for the performance of electronic equipment. For spacecraft, however,the severe aerodynamic heating and low-pressure environment have posed a serious challenge to the heat re-moval of the high-power electronic equipment. Spray cooling is considered to be an appropriate way to maintainthe temperature of the electronic devices within acceptable limits. This paper considers the heat balance in spraycooling using a First Law of Thermodynamics modelling approach as well as a thermal control strategy for asemi-enclosed electronic equipment cabin. Theoretical analysis and numerical results are presented to show theapplicability of the developed model and strategy. Characteristics of liquid nitrogen droplet heating, boiling andflash evaporation as well as spray patterns are discussed in detail. Furthermore, the control method of the spraynozzles switching and the interaction mechanism between pressure and temperature within the electronicequipment cabin during spray cooling are also addressed. The thermal control strategy and the model predic-tions presented in this work can help researchers and designers to ascertain optimum operational conditions ofspraying cooling, including the spray mass flow rate, the spray length and the distribution of the sprayed dro-plets.

1. Introduction

The performance of electronic equipment is very sensible to tem-perature and the heat generated by electronic circuitry must be

dissipated to prevent immediate failure and improve long-term relia-bility. In the field of near space aircraft, the thermal management ofhigh-power electronic equipment plays an important role in main-taining the flight safety and has gained a great deal of attention in

https://doi.org/10.1016/j.applthermaleng.2018.02.095Received 27 August 2017; Received in revised form 28 January 2018; Accepted 27 February 2018

⁎ Corresponding author.E-mail address: jiangpx@mail.tsinghua.edu.cn (P. Jiang).

Applied Thermal Engineering 136 (2018) 319–326

Available online 06 March 20181359-4311/ © 2018 Elsevier Ltd. All rights reserved.

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recent years [1–3]. However, the ambient conditions in near space haveposed a great challenge to the heat dissipation in the electronicequipment cabin (EEC). Near space is the region of earth’s atmospherethat lies between 20 and 100 km (65,000 and 328,000 feet) above sealevel. The typical properties of the area are characterized by lowpressure 5530–0.03 Pa, low atmospheric density 0.0889–5×10−7 kg/m3, and low temperature 216.65–210 K. For airship, the heat generatedby the electronic equipment can be transported into the near spaceenvironment by heat radiators, heat pipe, phase change material heatexchanger [4] and spray cooling [5], etc. For high-speed spacecraft, theaerodynamic heat flux on the aircraft fuselage could be far greater thanthe heat flux generated by the electronic equipment inside the cabin.Therefore, spray cooling could be the most appropriate approach toadjust the operating temperature of the electronic equipment withinacceptable limits for high-speed spacecraft. This work deals with spraycooling in a semi-closed cabin, which is filled with electronic equip-ment under low pressure. Considering the cooling capacity and elec-trical insulation, liquid nitrogen (LN2) is selected as the workingmedium.

Spray cooling is a technology that combines impact convection heattransfer and phase transition heat transfer, and is characterized by highheat dissipation rate, uniformity of heat removal and stable coolingperformance [6]. Therefore, spray cooling is of increasing interest forelectronic cooling and other high heat flux applications [7]. Kim re-viewed on the development of spray cooling technology prior to 2006and concluded that spray cooling mechanisms in both the single-phaseand two-phase regimes were not conclusively identified and furtheradvances in understanding of spray cooling required advanced experi-mental techniques e.g., very highspeed videos, to measure spray para-meters [7]. Two theories have been proposed to explain the mechanismof the spray cooling: thin film evaporation & convection [8] and sec-ondary nucleation [9]. The thin film evaporation & convection theoryindicates that spray produces a thin liquid film on the surface throughwhich the heat is conducted and this is further enhanced by the dropletimpact. The secondary nucleation theory indicates that sprayed dro-plets entrain vapor/gas into the liquid film, accelerating bubble nu-cleation and vigorous boiling within the film. Based on the two me-chanisms of spray cooling, surface treatment is applied to enhance the

heat removal rate. Sehmbey et al. [10,11] investigated the effects ofsurface roughness (0.05–0.15 μm) on the performance of spray coolingwith LN2 and found that increasing roughness greatly enhanced heattransfer performance. This conclusion was confirmed by Ortiz & Gon-zalez [12] and Zhang et al. [13]. Chen et al. [14] conducted an ex-perimental study of spray cooling on nanostructured surfaces and theysuggested that nanostructure promotes better wettability on surface,which in turn enhances the heat transfer rate and surface temperatureuniformity. Chen et al. [15] investigated spray parameters on criticalheat flux (CHF) and proved that the mean droplet velocity had the mostdominant effect on CHF, followed by the mean droplet flux, while theSauter mean diameter (d32) did not appear to have an effect on CHF. Itis noted that most of the existing studies intend to reveal the heattransfer mechanism of spray cooling from the perspectives of spraydroplet properties, heating surface structures, spray distance and in-clined angle, etc. [6]. And it is also noted that most researches arecarried out under normal pressure conditions. Different from the pre-vious studies, the current research is not directed against a specificheating surface, but for the thermal control of a large number of elec-tronic devices in a semi-enclosed cabin. In other words, the currentresearch object is at a more macro level and the spray cooling approachis applied to control the temperature of the electronic devices by re-ducing the gas temperature inside the cabin.

Another issue associated with the current spray cooling is low at-mospheric pressure (< 5530 Pa). It means that flash evaporation couldoccur during the process of LN2 releasing. Although the pressure in theEEC can be maintained at normal pressure 1 atm or even higher byapplying a relatively thick skin, this will increase the weight and sa-crifice the flight speed of spacecraft. On flash spray cooling (FSC),Yanosy [16] and Aoki [17] conducted experiments on the phenomenonand heat transfer of FSC. They found that the heat removal rate shows acloser relationship with the sprayed droplet size and the superheatdegree. Afterward, Marcos et al. [18] conducted another FSC test withwater and found that water spray cooling at reduced system pressurecan significantly decrease the surface temperature as compared toambient pressure spray cooling. More recently, Cheng et al. [19] de-veloped a mathematic model describing the heat & mass transfer duringspray cooling, in which the liquid flash evaporation was considered.

Nomenclature

A area, m2

C constantcp, cpr, cpl heat capacity, J/(kg K)Cw,s, Cw,∞ vapor concentration, kmol/m3

d droplet diameter, mEEC electronic equipment cabing Standard acceleration of gravity, 9.8 N/kghfg latent heat, J/kgh heat transfer coefficient, W/(m2 K)kc mass transfer coefficient, m/sl characteristic length, mLN2 liquid nitrogenm mass, kgM molecular weight, kg/kmolN-HTC natural convection heat transfer coefficientn constant; molecule quantity, molNu Nussel numberP, P0, Pext pressure, PaPr Prandtl numberq heat flux, Wqm, qm,g mass flow rate, kg/sr droplet radius, mR universal gas constant, 8.314×103 J/(mol K)

T, Td, Tl, Tw, Tθ, Tsat temperature, Kt time, sGr Grashov numberXi mole fraction of species

Greek symbols

α thermal expansion coefficientε emissivityλ, λd conductivity, W/(m K)μ molecular viscosity, Pa sπ constant, 3.1416ρ, ρd density, kg/m3σ Stefan-Boltzmann constant, 5.67×10−8 W/(m2 K4)γ specific heat capacity ratio

Subscripts

0 initiald dropletext externall liquidm masssat saturationw wall

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Most recently, Wang et al. [20] conducted an experimental study onwater spray cooling in a vacuum chamber and found that the ambientpressure affects the cooling performance when flashing boiling occurs,but this effect becomes negligible in the subcooled spray cooling. In theprevious study of this article, we utilize numerical approach to predictsingle water droplet phase transition and lifetime during FSC [21]. It isfound that the ambient pressure has relatively little effect on dropletlifetime compared to temperature and droplet size. The sprayed dropletwill exist for a long time if the droplet diameter is larger and the am-bient temperature is lower. In this work, droplet lifetime is still aconcerned issue.

Literature research indicates that the thermal control of an elec-tronic equipment cabin by spray cooling under low pressure is less re-ported and the interaction mechanism between pressure and tempera-ture within the EEC during spray cooling is not well understood. Thispaper is concerned with the vacuum spray cooling in an EEC by usingLN2 and a mathematical model is developed to investigate the heat andmass transfer and pressure changes during spray cooling. One aim ofthis work is to propose an algorithm and a control-system concept tomaintain the temperature of electronic devices in the cabin within ac-ceptable limits. The physical model applied in this paper is a semi-en-closed cabin filled with electronic devices. The pressure of the cabin isinfluenced by spray cooling and adjusted by turning on/off the bleedvalve. The contents are organized as follows: First, the natural con-vection under low pressure is analyzed; Second, a thermodynamicsmodel as well as a strategy for controlling the pressure and temperatureinside the EEC are presented; And then, calculations on LN2 spraycooling, including LN2 droplet vaporization, continuous spray and in-termittent spray, are expanded; Finally, main conclusions are drawn.

2. Analytical model

The structure of the EEC model is shown in Fig. 1. It mainly includesone LN2 inlet, one gas outlet, valves, the atomizing nozzles and theelectronic devices which are also the heat source. The cabin is assumedto be located in near space and the ambient pressure is less than5530 Pa. The pressure and temperature within the EEC are adjusted byLN2 spray and gas releasing. For the current work, the following majorassumptions are employed in the derivation of the governing equations:(1) the air and LN2 vapor inside the EEC behaves as ideal gases; (2) thespray nozzles are arranged well enough and the ambient temperaturewithin the EEC is equal everywhere during spray cooling; (3) spraycooling approach is applied to control the temperature of the electronicdevices by reducing the gas temperature inside the cabin, and inter-action between the spray droplets and the wall surface, however, is notthe interest of this article.

2.1. Natural convection under low pressure

The desired operating temperature of electronic equipment Tw isusually in the range −40 °C to 50 °C. Tw can be obtained by solving asimple heat balance equation:

= +T Tq

hAw (1)

where T is the ambient temperature inside the EEC which is controlledby spray cooling, q denotes the heat flux provided by the electronicdevices, h is the convection heat transfer coefficient, A is the surfacearea of electronic devices. When q and A are fixed, Tw depends on theambient temperature T and the heat transfer coefficient h.

As the pressure of the cabin is very low, the heat removal is mainlyby natural convection. The Nussel number Nu in natural convectiontakes the following form:

=Nu C Gr Pr( )n (2)

where C and n are constants determined by experiment [22] and given

in Table 1. Gr and Pr are Grashov and Prandtl numbers, which areexpressed as:

= =Grgα Tl

μ ρPr

μcλ

Δ( / )

, p3

2 (3)

where g is Standard acceleration of gravity, α is the coefficient ofthermal expansion and for an ideal gas α=1/T; l is the characteristiclength of the electronic device, μ and ρ denote the air dynamic viscosityand density, cp and λ denote the heat capacity and thermal conductivityof air.

It is noted that the changes of air dynamic viscosity, thermal ca-pacity and conductivity can be safely ignored under reduced pressurewhen the ambient temperature is held constant. Therefore, the dete-rioration of heat transfer under low pressure can be estimated from thefollowing equation:

⎜ ⎟ ⎜ ⎟≈ ⎛⎝

⎞⎠

= ⎛⎝

⎞⎠

NuNu

ρρ

PP

n n

0 0

2

0

2

(4)

where the subscript 0 denotes air density and pressure at normalpressure ∼100 kPa. Using Eq. (4), we can evaluate the heat transfercoefficient under low pressure. For example, at 1 atm (100 kPa), thenormal range of natural convection heat transfer coefficient (N-HTC) isbetween 1 and 10W/(m2 K), while at P=10 kPa, the N-HTC is reducedto 0.2–2W/(m2 K). Once N-HTC is obtained, the desired ambient tem-perature T within the EEC can be determined, because Tw, q and A areusually provided as known conditions.

2.2. Heat and pressure balance during spray cooling

The heat generated by the electronic devices is absorbed by thespray LN2 and air inside the cabin, thus the heat balance equation canbe written as:

= − + − + +q q c T T c T T h mc dTdt

[ ( ) ( ) ]m pr sat pl l sat fg p (5)

where m denotes the mass of the gas in EEC, dt denotes the time step, qmdenotes the mass flow rate of LN2, cpl and cpr denote the specific heatcapacities of LN2 and LN2 vapor, respectively; Tl denotes the tempera-ture of LN2 relative to the saturation temperature Tsat; hfg denotes thelatent heat of LN2.

According to the ideal gas law, the pressure changes due to spraycooling can be calculated from:

=+ + +P P n n T T( / )( / )i i i i i i1 1 1 (6)

where n denotes the quantity of gas molecules in mol. The superscript i

Fig. 1. Schematic of the model structure.

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and i + 1 denotes the time step.The gas flow from the outlet of the EEC is deemed as an isentropic

process, then the gas velocity v and mass flow rate qm,g are calculatedby:

⎜ ⎟=−

⎡

⎣

⎢⎢

−⎛⎝

⎞⎠

⎤

⎦

⎥⎥

−

vγ

γPρ

PP

21

1ext

γγ

1

(7)

=−

⎡

⎣⎢⎢

⎛⎝

⎞⎠

−⎛⎝

⎞⎠

⎤

⎦⎥⎥

+

q ρAγ

γPρ

PP

PP

21m g

ext γ extγ

γ,

2 1

(8)

where Pext denotes the pressure at the outlet of the EEC, γ denotes thespecific heat capacity ratio of the gas within the EEC.

Note that in Eq. (5), we assume all the LN2 sprayed into the EEC iscompletely vaporized in one time step dt, and therefore the time stepmust be determined properly in order to get a more accurate result.Obviously, the time required for the sprayed LN2 to evaporate dependson the lifetime of the sprayed droplets. In order to get the time requiredfor complete evaporation, the heat and mass transfer between dropletand its surroundings should be calculated in advance.

2.3. Droplet heat and mass transfer

In this work, three typical vaporization processes are identified:heating evaporation (droplet temperature Td < Tsat), boiling(Td= Tsat) and flash evaporation (Td > Tsat). For droplet heating eva-poration and boiling (mode ①) as shown in Fig. 2, the droplet tem-perature could perform an increasing tendency with time, but it willnever surpass the saturation line. For flash evaporation, however, manyfactors, including the ambient temperature and the mole fraction ofdroplet species, affect the variation of the droplet temperature withtime [21]. Three typical distributions are depicted in Fig. 2: the droplettemperature drops rapidly over/below the saturation line (modes ② and③), or first rises and then drops (mode ④). It is found that the diffusioncontrolled model based on Fick’s law of diffusion can be used to de-scribe the process of droplet flash evaporation [21]:

= − − ∞drdt

Mρ

k C C( )d

c w s w, ,(9)

where r and ρd denote the radius and density of the droplet, M denotesthe molecular weight of droplet vapor, kc denotes the mass transfercoefficient which can be obtained from the Sherwood number corre-lation [21,23–24], Cw,s and Cw,∞ denote the vapor concentration atdroplet surface and in the bulk gas, respectively:

= =∞CPRT

C X PRT

,w s satd

w i, , (10)

here Xi is the local bulk mole fraction of species, R is the universal gasconstant.

The droplet temperature is updated according to a heat balance thatrelates the sensible heat change in the droplet to the convective andlatent heat transfer between the droplet and the continuous phase:

= ⎡⎣⎢

+− + − − ⎤

⎦⎥

dTdt ρ c r

λ Rer

T T εσ T T ρ h drdt

3 (1 0.23 ) ( ) ( )dd p d

d dd θ d d fg

,

4 4

(11)

where cp,d is droplet heat capacity, λd is the thermal conductivity of thedroplets, Red is the relative Reynolds number, ε denotes the dropletemissivity, σ denotes Stefan-Boltzmann constant (5.67× 10−8 W/m2 K4), Tθ is radiation temperature, it approximately equals to theelectronic device temperature Tw.

When droplet is heated to the boiling temperature Tsat, the item ofthe sensible heat in Eq. (11) can be dismissed, then yields:

= ⎡⎣⎢

+− + − ⎤

⎦⎥

drdt ρ h

λ Rer

T T εσ T T1(1 0.23 )

( ) ( )d fg

d dd θ d

4 4

(12)

2.4. Thermal control strategy

The strategy for the pressure and temperature control inside the EECis shown in Fig. 3. The detailed operating procedures are as follows:

(1) Determine the upper and lower limits of the air temperature, Tupand Tdw, and pressure, Pup and Pdw, of the EEC by applying Eqs.(1)–(4).

(2) Calculate the heat and mass transfer between droplets and thesurroundings by Eqs. (9)–(12) to determine the time step of itera-tion.

(3) Solve Eqs. (5)–(8) to obtain the transit temperature and pressurechanges with time during spray.

(4) Thermal Management: monitor the gas temperature inside the EEC.If the gas temperature is higher than the upper limit, then turn onthe spraying nozzles to reduce the cabin temperature; else if the airtemperature is below the lower limit, turn off the spray nozzles tosave LN2. The order of the loop is ①→②→③→① as shown in thelower right corner of Fig. 3.

(5) Pressure Control: monitor the pressure of the EEC. If the pressure ishigher than the upper limit, then turn on the vent valve to deflategas; else if the pressure is below the lower limit, turn off the ventvalve to collect gas. The order of the loop is ④→⑤→⑥→④ asshown in the upper left corner of Fig. 3. In addition, the dashedlines ⑦ and ⑧ indicate that the processes of deflation and LN2 spraycould cause indirect effects on the temperature and pressure controlprocesses.

3. Results and discussion

In this section, droplet vaporization under low pressure and char-acteristics of the continuous and intermittent spray cooling will bediscussed. Furthermore, the effects of temperature and pressure limitson spray frequency are also addressed.

Table 1C and n in Eq. (2).

Flow pattern C n

Laminar 0.48 1/4Transition 0.0445 0.37Turbulent 0.10 1/3

Fig. 2. Typical modes of droplet vaporization.

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Fig. 3. Schematic diagram of the temperature and pressure control of the electronicequipment cabin.

Fig. 4. Droplet lifetime vs droplet diameter.

Fig. 5. Variation of droplet diameter with time (Ambient Pressure P0= 101325 Pa,Temperature T∞= Td=288 K, Relative humidity (RH) 60% and the mole fraction ofwater vapor Xi=0.011; ρa=1.23 kg/m3, ρL=999.5 kg/m3, Droplet Reynolds numberRe=0.002(d0= 10 μm), 0.016(d0= 20 μm), 0.052(d0= 30 μm), 0.12(d0= 40 μm),0.23(d0= 50 μm), 0.72(d0= 75 μm), 1.6(d0= 100 μm), 4.5(d0= 150 μm),9.2(d0= 200 μm)).

Fig. 6. Variation of droplet lifetime with diameter, ambient pressure and temperature.

Fig. 7. Variation of droplet lifetime with diameter, ambient pressure and temperature(droplet diameter d0= 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 75 μm, 100 μm, 150 μm,200 μm; And the corresponding Reynolds number Re=19, 38, 57, 76, 95, 143, 191, 286,382; Mole fraction of LN2 vapor Xi=1; Initial droplet temperature Td=70 K).

Fig. 8. EEC transient temperature and pressure at qm=1.5× 10−3 kg/s and1.7× 10−3 kg/s.

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3.1. LN2 droplet vaporization

Validation of the droplet evaporation model is expanded prior tocalculation of the LN2 droplet vaporization. Fig. 4 shows the compar-ison of the lifetime predicted by Eqs. (9)–(12) with the data provided byHolterman [25] for water droplet at 1 atm (100 kPa). The current pre-dictions show perfect agreement with Holterman’s data. It is noted thatthe droplet lifetime increases exponentially with the increase of droplet

diameter. Variation of the droplet diameter with time during evapora-tion was expressed as the ratio of the transit droplet diameter d to theinitial droplet diameter d0 and the results are as shown in Fig. 5. It’sseen that the droplet diameter drops rapidly with time especially for thesmaller droplet. In addition, test of the model capacity in predictingdroplet temperature changes under flash evaporation has been pre-sented prior to this work [21] and it’s observed that the model pre-dictions are in good agreement with the experimental data provided byShin [26] and Li [27]. As the data on the spray cooling of an electroniccabin under low pressure is less reported, the model was only verifiedby comparing the predicted results with the published data of dropletvaporization. Despite this, the predictions are reliable as the modelcorrelations are developed based on the classical heat & mass transferand thermodynamics theories, which have been verified thoroughly.

For LN2 droplet vaporization, as the initial component ratio of ni-trogen inside the cabin is about 78% (Xi≥ 0.78) and this value will stillincrease with LN2 spray cooling, thus the calculation of droplet lifetimewas expanded at Xi=1 in order to get the limit of droplet lifetime.Other calculation conditions are listed in the upper right corner ofFig. 6. Typical types of LN2 droplet vaporization—including heatingevaporation, boiling and flash evaporation—are demonstrated in thefigure. It is seen that the time required from heating to boiling is veryshort and the droplet temperature rises to saturation in a nearly straightway. For flash evaporation, however, the droplet temperature reducesrapidly to a relatively stable level. One point should be noted that the

Fig. 9. Variation of N2 concentration and the outlet velocity with spray time.

Fig. 10. EEC transient temperature and pressure at qm=1.9× 10−3 kg/s and2.5×10−3 kg/s.

Fig. 11. LN2 spray frequency for different limits of temperature control(qm=2.0× 10−3 kg/s).

Fig. 12. Consumption of liquid nitrogen at different mass flow rate.

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pressure and temperature of LN2 at the triple point are 12.5 kPa and63.14 K, respectively, that is during the whole flash evaporation pro-cess, the droplet temperature is always over the saturation temperature.

The curves in Fig. 7(a) show the variation of LN2 droplet lifetimewith increasing diameter at P=100 kPa, 50 kPa, 10 kPa, 5 kPa and theambient temperature is fixed at 300 K. Correspondingly, the results inFig. 7(b) are obtained at T=350 K, 320 K, 280 K, 250 K and the am-bient pressure is fixed at 10 kPa. It is observed that the ambient pres-sure has little effect on droplet lifetime especially for the droplets withdiameter less than 100 μm. While the droplet lifetime is significantlyaffected by the ambient temperature especially for the droplets withdiameter larger than 50 μm. The results indicate that droplet with largerdiameter tends to have a relatively long lifetime especially when theambient temperature is lower. Obviously, the lifetime of the LN2 dro-plet is much shorter than that of the water droplet as shown in Fig. 4.Under the current calculation conditions, the longest lifetime is about170ms at d0= 200 μm and T=250 K. Assume that the sprayed dropletdiameter is no more than 200 μm, and then the time step is fixed at170ms can guarantee the accuracy of iteration.

For spray cooling, once the droplet lifetime is obtained, the iterationtime step for solving the heat and mass transfer equation can be de-termined accordingly. In the current work, the diameter of the sprayeddroplets is assumed to be less than 200 μm, thus the time step is fixed at170ms according to Fig. 7. The time required for the exhaust valveopening and closing twice is defined as the total calculation time. If nootherwise specified, the following conditions are applied in solving themodel:

• Net volume of the EEC:1m3

• Temperature upper limit, Tup: 320 K

• Outlet diameter: 20mm • Pressure upper limit, Pup: 20 kPa• Heat flux: 1.0 kW • Temperature lower limit, Tdn: 260 K• Initial ambient

temperature: 350 K• Pressure lower limit, Pdn: 10 kPa

• Initial ambient pressure:2.5 kPa

• Inlet temperature of LN2: 70 K

• Initial mole fraction ofN2: 0.78

• Mass flow rate of LN2, qm:1.5× 10−3–3.5×10−3 kg/s

3.2. Continuous spray

Once the spray nozzles are opened, the LN2 spray will not stop untilthe gas temperature within the EEC reaches the lower limitTdn=260 K. Fig. 8 shows the transit temperature and pressure changeswith time at qm=1.5×10−3 kg/s and qm=1.7×10−3 kg/s. It is seenthat at qm=1.5× 10−3 kg/s, the gas temperature rises as the sprayedLN2 cannot completely absorb the heat generated by the electronicdevices. When the mass flow rate of LN2 increases toqm=1.7× 10−3 kg/s, the temperature reduces from 350 K to 300 K inabout 290 s. The pressure performs a near-linearly increasing and de-creasing distribution during spray cooling.

The concentration fraction of N2 increases during spray cooling asshown in Fig. 9, and the cabin is almost full of N2 at the end of thespray. The exhaust velocities are also plotted in the figure. It is seen thatthe exhaust velocity is from 60m/s to 50m/s at qm=1.5× 10−3 kg/s,while at qm=1.7× 10−3 kg/s, the exhaust velocity becomes reducedfrom 53m/s to 45m/s due to the relatively low temperature of the gas.

3.3. Intermittent spray

When the mass flow increases to qm=1.9×10−3 kg/s andqm=2.5× 10−3 kg/s, the gas temperature of the EEC researches to thelower limit rapidly, the results are as shown in Fig. 10(a) and (b), re-spectively. Compare the temperature data in Fig. 10(a) with the resultsin Fig. 8, it is found that although the increment of the mass flow rate ofLN2 is only 0.2 g/s, the gas temperature is reduced from 365 K to 260 K

in about 45 s. Furthermore, it is noted that when the mass flow rateincreases from qm=1.9× 10−3 kg/s to qm=2.5× 10−3 kg/s, theswitching frequency of the spray nozzles also increases from 3 times to11 times. This is because the heating flux is relatively high while themass of the gas is small due to the low pressure, which leads to the gastemperature rising to the upper limit Tup rapidly. And the high coolingcapacity of LN2 also accounts for the increase of the switching fre-quency of the spray nozzles. In addition, pressure fluctuations are ob-served during the switching of the spray nozzles. Comparing the data ofFig. 10(a) and (b), it is found that the larger the mass flow, the greaterthe pressure fluctuation. However, the pressure fluctuations seem tohave little effect on the variation of the gas temperature.

As is known that switching the spray nozzles frequently could pose agreat challenge for the service life of the spray nozzles and the pressurefluctuation induced by the frequently switching may cause a potentialdestructive effect on the performance of the electronic devices.Therefore, as long as the cooling effect can be guaranteed, the switchingfrequency of the spray nozzles is expected to be as low as possible. Anobvious way to reduce the switching frequency is to cut down the massflow rate of LN2 as shown in Figs. 8 and 10(a, b). Another way to reducethe switching frequency is to modify the limits of the temperaturecontrol as shown in Fig. 11. When the range of the temperature controlis changed from 260–320 K to 220–280 K, the switching frequency ofthe spray nozzles is reduced from 6 to 2 times. Additionally, increasingthe upper limit of pressure control can also increase the time requiredfor switching the spray nozzles. Take the results in Fig. 10(b) as anexample, in the first 110 s the switching time interval increases from 8 s(segment a) to 33 s (segment b) with the pressure rises from 2.5 kPa to20 kPa.

The consumption of LN2 is another important parameter that con-cerned in this work. An average consumption rate qm is introduced toevaluate the LN2 required if the mass flow rate changes. The averageconsumption rate qm is defined as the sum of LN2 mass imported intothe EEC divided by the total time. Fig. 12 shows the value of theaverage consumption rate at the mass flow rates of 1.9× 10−3 kg/s,2.2× 10−3 kg/s, 2.5× 10−3 kg/s and 3.0× 10−3 kg/s. It is seen thatalthough the mass flow rate of LN2 increases from 1.9× 10−3 kg/s to3.0×10−3 kg/s, the distribution of qm performs a stable tendency andthe level is fixed in a narrow range of 1.7× 10−3–1.8×10−3 kg/s. Thereason is that once the heat load of the cabin is fixed, the quantity ofLN2 required for the heat removal mainly depends on the limits oftemperature and pressure.

4. Conclusions

A generic mathematical transient model as well as a control-systemconcept to maintain the temperature of the electronic devices in thecabin within acceptable limits was developed. The algorithm is dividedinto the following three steps: ① calculate the convective heat transfercoefficient of the electronic devices to obtain the limits of the tem-perature control; ② solve the model correlations of droplet vaporizationto determine the length of the time step for the transient calculation; ③expand the iteration on the heat & mass transfer of spray cooling to getthe transit temperature and pressure during the spray cooling. The mainconclusions are drawn as:

(1) The predictions indicate that droplet with larger diameter tends tohave a relatively long lifetime, but a higher ambient temperaturewill reduce the lifetime of the droplet. For liquid nitrogen droplet,flash evaporation under low pressure seems to have little effect ondroplet lifetime.

(2) The spraying modes like continuous spray and intermittent spraycan be obtained by adjusting the mass flow rate of liquid nitrogen.For the intermittent spray, the switching frequency of the spraynozzles increases with increasing mass flow rate of LN2.

(3) The switching frequency of the spray nozzles is influenced greatly

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by the limits of the temperature control. Reducing the lower limit oftemperature control will produce a low frequency of the spraynozzles switching. In addition, increasing the upper limit of pres-sure control can also reduce the spray nozzles switching frequency.

Acknowledgement

This work was financially supported by National Natural ScienceFoundation (Grant No. 51606108), the Science Fund for CreativeResearch Groups of NSFC (No. 51621062) and the China PostdoctoralScience Foundation (No. 2016M601023). The authors would like tothank Prof. Yinhai Zhu and Dr. Xiaolong Ouyang for their many con-tributions to this research.

References

[1] F.F. Chen, W.F. Tam, N.R. Shimp, et al., An innovative thermal management systemfor a Mach 4 to Mach 8 hypersonic scramjet engine, AIAA Paper, vol. 3734, 1998.

[2] H. Taguchi, H. Kobayashi, T. Kojima, et al., Research on hypersonic aircraft usingpre-cooled turbojet engines, Acta Astronaut. 73 (2012) 164–172.

[3] J. Qin, S. Zhang, W. Bao, et al., Thermal management method of fuel in advancedaeroengines, Energy 49 (2013) 459–468.

[4] A. Sharma, V.V. Tyagi, C.R. Chen, et al., Review on thermal energy storage withphase change materials and applications, Renew. Sustain. Energy Rev. 13 (2)(2009) 318–345.

[5] E.A. Silk, E.L. Golliher, R.P. Selvam, Spray cooling heat transfer: technology over-view and assessment of future challenges for micro-gravity application, EnergyConvers. Manage. 49 (3) (2008) 453–468.

[6] G. Liang, I. Mudawar, Review of spray cooling–Part 1: single-phase and nucleateboiling regimes, and critical heat flux, Int. J. Heat Mass Transf. 115 (2017)1174–1205.

[7] J. Kim, Spray cooling heat transfer: the state of the art, Int. J. Heat Fluid Flow 28 (4)(2007) 753–767.

[8] L.C. Chow, E.T. Maheikey, Surface roughness and its effects on the heat transfermechanism in spray cooling, J. Heat Transf. 114 (1992) 211–219.

[9] D.P. Rini, R.H. Chen, L.C. Chow, Bubble behavior and nucleate boiling heat transferin saturated FC-72 spray cooling, Trans.-Am. Soc. Mech. Eng. J. Heat Transf. 124 (1)

(2002) 63–72.[10] M.S. Sehmbey, L.C. Chow, O.J. Hahn, et al., Effect of spray characteristics on spray

cooling with liquid nitrogen, J. Thermophys. Heat Transf. 9 (4) (1995) 757–765.[11] M.S. Sehmbey, L.C. Chow, O.J. Hahn, et al., Spray cooling of power electronics at

cryogenic temperatures, J. Thermophys. Heat Transf. 9 (1) (1995) 123–128.[12] L. Ortiz, J.E. Gonzalez, Experiments on steady-state high heat fluxes using spray

cooling, Exp. Heat Transf. 12 (3) (1999) 215–233.[13] Z. Zhang, J. Li, P.X. Jiang, Experimental investigation of spray cooling on flat and

enhanced surfaces, Appl. Therm. Eng. 51 (1) (2013) 102–111.[14] J. Chen, Z. Zhang, X. Ouyang, et al., Dropwise evaporative cooling of heated sur-

faces with various wettability characteristics obtained by nanostructure modifica-tions, Nanoscale Res. Lett. 11 (1) (2016) 158.

[15] R.H. Chen, L.C. Chow, J.E. Navedo, Effects of spray characteristics on critical heatflux in subcooled water spray cooling, Int. J. Heat Mass Transf. 45 (19) (2002)4033–4043.

[16] J.L. Yanosy, Water Spray Cooling in a Vacuum, Ph.D. dissertation, The University ofConnecticut, 1985.

[17] I. Aoki, Analysis of characteristics of water flash evaporation under low-pressureconditions, Heat Transf.—Asian Res. 29 (1) (2000) 22–33.

[18] A. Marcos, L.C. Chow, J.H. Du, et al., Spray cooling at low system pressure, in:Semiconductor Thermal Measurement and Management, 2002, Eighteenth AnnualIEEE Symposium, IEEE, 2002, pp. 169–175.

[19] W. Cheng, H. Chen, L. Hu, et al., Effect of droplet flash evaporation on vacuum flashevaporation cooling: modeling, Int. J. Heat Mass Transf. 84 (2015) 149–157.

[20] J.X. Wang, Y.Z. Li, X.K. Yu, et al., Investigation of heat transfer mechanism of lowenvironmental pressure large-space spray cooling for near-space flight systems, Int.J. Heat Mass Transf. 119 (2018) 496–507.

[21] C. Wang, R. Xu, Y. Song, et al., Study on water droplet flash evaporation in vacuumspray cooling, Int. J. Heat Mass Transf. 112 (2017) 279–288.

[22] S.M. Yang, Improvement of the basic correlating equations and transition criteria ofnatural convection heat transfer, Heat Transf.—Asian Res. 30 (4) (2001) 293–300.

[23] W.E. Ranz, W.R. Marshall, Evaporation from drops, Chem. Eng. Prog 48 (3) (1952)141–146.

[24] W.E. Ranz, W.R. Marshall Jr, Evaporation from drops, Part I and Part II, Chem. Eng.Prog 48 (4) (1952) 173–180.

[25] H.J. Holterman, Kinetics and Evaporation of Water Drops in Air, IMAG,Wageningen, NL, 2003.

[26] H.T. Shin, Y.P. Lee, J. Jurng, Spherical-shaped ice particle production by sprayingwater in a vacuum chamber, Appl. Therm. Eng. 20 (5) (2000) 439–454.

[27] X.W. Li, X.S. Zhang, S. Quan, Evaporative supercooling method for ice production,Appl. Therm. Eng. 37 (2012) 120–128.

C. Wang et al. Applied Thermal Engineering 136 (2018) 319–326

326

http://refhub.elsevier.com/S1359-4311(17)35566-7/h0010http://refhub.elsevier.com/S1359-4311(17)35566-7/h0010http://refhub.elsevier.com/S1359-4311(17)35566-7/h0015http://refhub.elsevier.com/S1359-4311(17)35566-7/h0015http://refhub.elsevier.com/S1359-4311(17)35566-7/h0020http://refhub.elsevier.com/S1359-4311(17)35566-7/h0020http://refhub.elsevier.com/S1359-4311(17)35566-7/h0020http://refhub.elsevier.com/S1359-4311(17)35566-7/h0025http://refhub.elsevier.com/S1359-4311(17)35566-7/h0025http://refhub.elsevier.com/S1359-4311(17)35566-7/h0025http://refhub.elsevier.com/S1359-4311(17)35566-7/h0030http://refhub.elsevier.com/S1359-4311(17)35566-7/h0030http://refhub.elsevier.com/S1359-4311(17)35566-7/h0030http://refhub.elsevier.com/S1359-4311(17)35566-7/h0035http://refhub.elsevier.com/S1359-4311(17)35566-7/h0035http://refhub.elsevier.com/S1359-4311(17)35566-7/h0040http://refhub.elsevier.com/S1359-4311(17)35566-7/h0040http://refhub.elsevier.com/S1359-4311(17)35566-7/h0045http://refhub.elsevier.com/S1359-4311(17)35566-7/h0045http://refhub.elsevier.com/S1359-4311(17)35566-7/h0045http://refhub.elsevier.com/S1359-4311(17)35566-7/h0050http://refhub.elsevier.com/S1359-4311(17)35566-7/h0050http://refhub.elsevier.com/S1359-4311(17)35566-7/h0055http://refhub.elsevier.com/S1359-4311(17)35566-7/h0055http://refhub.elsevier.com/S1359-4311(17)35566-7/h0060http://refhub.elsevier.com/S1359-4311(17)35566-7/h0060http://refhub.elsevier.com/S1359-4311(17)35566-7/h0065http://refhub.elsevier.com/S1359-4311(17)35566-7/h0065http://refhub.elsevier.com/S1359-4311(17)35566-7/h0070http://refhub.elsevier.com/S1359-4311(17)35566-7/h0070http://refhub.elsevier.com/S1359-4311(17)35566-7/h0070http://refhub.elsevier.com/S1359-4311(17)35566-7/h0075http://refhub.elsevier.com/S1359-4311(17)35566-7/h0075http://refhub.elsevier.com/S1359-4311(17)35566-7/h0075http://refhub.elsevier.com/S1359-4311(17)35566-7/h0085http://refhub.elsevier.com/S1359-4311(17)35566-7/h0085http://refhub.elsevier.com/S1359-4311(17)35566-7/h0095http://refhub.elsevier.com/S1359-4311(17)35566-7/h0095http://refhub.elsevier.com/S1359-4311(17)35566-7/h0100http://refhub.elsevier.com/S1359-4311(17)35566-7/h0100http://refhub.elsevier.com/S1359-4311(17)35566-7/h0100http://refhub.elsevier.com/S1359-4311(17)35566-7/h0105http://refhub.elsevier.com/S1359-4311(17)35566-7/h0105http://refhub.elsevier.com/S1359-4311(17)35566-7/h0110http://refhub.elsevier.com/S1359-4311(17)35566-7/h0110http://refhub.elsevier.com/S1359-4311(17)35566-7/h0115http://refhub.elsevier.com/S1359-4311(17)35566-7/h0115http://refhub.elsevier.com/S1359-4311(17)35566-7/h0120http://refhub.elsevier.com/S1359-4311(17)35566-7/h0120http://refhub.elsevier.com/S1359-4311(17)35566-7/h0125http://refhub.elsevier.com/S1359-4311(17)35566-7/h0125http://refhub.elsevier.com/S1359-4311(17)35566-7/h0130http://refhub.elsevier.com/S1359-4311(17)35566-7/h0130http://refhub.elsevier.com/S1359-4311(17)35566-7/h0135http://refhub.elsevier.com/S1359-4311(17)35566-7/h0135

Modelling of liquid nitrogen spray cooling in an electronic equipment cabin under low pressureIntroductionAnalytical modelNatural convection under low pressureHeat and pressure balance during spray coolingDroplet heat and mass transferThermal control strategy

Results and discussionLN2 droplet vaporizationContinuous sprayIntermittent spray

ConclusionsAcknowledgementReferences