International Journal of Heat and Mass Transfer 79 (2014) 618–627

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Experimental study on static flash vaporization of aqueous NaCl solutionat different flash speed: Steam-carrying effect

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.08.0770017-9310/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel./fax: +86 (29) 8266 5741.E-mail address: yanjj@mail.xjtu.edu.cn (J. Yan).

1 Tel./fax: +86 (29) 8266 5741.

Dan Zhang 1, Bingchao Zhao 1, Junjie Yan ⇑, Qingzhong Yang 1

State Key Laboratory of Multiphase Flow in Power Engineering, School of Energy & Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China

a r t i c l e i n f o a b s t r a c t

Article history:Received 12 March 2014Received in revised form 27 August 2014Accepted 27 August 2014

Keywords:Static flashAqueous NaCl solutionFlash speedSteam-carrying effectHeight drop of waterfilmEquilibrium salt concentration of waterfilm

Flash speed was defined as mean decreasing rate of non-equilibrium fraction during fast evaporationstage. Experimental study on steam-carrying effect during static flash at different flash speed was carriedout. Different flash speeds were generated by installing thin orifice plates with different diameters(5–80 mm) between flash and vacuum chamber. Steam-carrying ratio was defined as mass ratio ofentrained liquid to flash steam. Results suggested that, first, accelerating flash speed could significantlyincrease steam-carrying ratio. Second, a peak value of steam-carrying ratio existed with increasing super-heat, but the peak value quickly dropped with shrinking orifice diameters. Third, due to steam-carryingeffect, increasing flash speed aggravated height drop of waterfilm during flash, but had nearly no influ-ences on equilibrium salt concentration of waterfilm. At last, an enhanced model for steam-carryingeffect during static flash at different flash speed was set up, depend on which, steam-carrying ratio,height drop of waterfilm as well as equilibrium salt concentration of waterfilm could be computed withinacceptable error range.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

If a superheated water film is exposed to a sudden pressuredrop below its saturation pressure, a quick and severe vaporizationtakes place, leading to significant temperature drop of waterfilmand massive vapor generation, and at the same time, some liquidis entrained away by flash steam through steam-carrying effect.This phenomenon is named flash vaporization and could be classi-fied into circulatory flash or static flash according to whether thewaterfilm has a velocity in horizontal direction. Flash is a complexphenomenon including both heat and mass transfer. The heattransfer is induced by the vaporization only, but the mass transferis caused by both vaporization and steam-carrying effect. Flash haswide application due to its good performance on energy conversionand separation, such as geothermal power plant [1], desalination[2], and so on. Therefore, its mechanism and properties, especiallythe heat transfer properties, are widely studied by scholars.

Static flash was selected as prototype to examine the basicmechanism and properties of flash vaporization. Miyatake et al.[3,4] carried out experiments on static flash of pure water withsuperheats varying between 3 and 5 K. Result indicated that

waterfilm temperature dropped quickly and significantly at thebeginning, then slowed down and finally reached at certain equi-librium value. Depending on this temperature evolution, theydivided flash into fast evaporation stage and gradual evaporationstage. Further, they also defined the saturation temperature corre-sponding to final equilibrium flash chamber pressure as theoreticalequilibrium temperature of waterfilm (Ts). Upon this assumption,they introduced superheat and non-equilibrium fraction (NEF, willbe introduced in detail in Section 2.2) to respectively measureunstable energy contained in waterfilm and the degree of comple-tion for flash. Based on these concepts, Miyatake et al. mainlyexamined heat transfer properties in fast evaporation stage. Resultsuggested that higher superheat or lower initial height of water-film led flash to take place faster and evaporate more completely.Saury et al. [5] also examined static flash of pure water, butenlarged superheat to between 1 and 35 K. Results suggested thatthe sensible heat released in the temperature drop of waterfilmcould be considered to all change into the latent heat of generatedsteam. Saury et al. [6] also slowed down the depressurization rateof flash chamber by installing adjusting valve between flash cham-ber and vacuum chamber and validated that it was an effectiveway to control and regulate flash speed, but the depressurizationrate had nearly nothing to do with final evaporated mass. Kim[7] further examined static flash of pure water and revealed severalcritical transition points in temperature evolutions of waterfilm.

Nomenclature

A cross-section area of flash chamber (m2)C steam-carrying coefficient (s6 kg�1 m�3)Cf drag force coefficient (–)cp specific heat of water at constant pressure (kJ kg�1 K�1)D orifice diameter (m)e error (–)F buoyancy (N)f drag force (N)fm salt concentration (mass fraction) of waterfilm (–)fps frame per second (–)FS flash speed (s�1)g acceleration of gravity (m s�2)H height of waterfilm (m)Ja Jacob number (–)K steam-carrying ratio (–)m mass (kg)N theoretical maximum number of droplet carried by unit

mass of steam (–)NEF non-equilibrium fraction (–)p pressure (MPa)r latent heat of vaporization (kJ kg�1)T temperature (�C)u speed of flash steam (m s�1)

Greek symbolsh boiling point elevation (�C)DH height drop of waterfilm (m)

DT superheat (K)n ratio of actual entrained mass to theoretical maximum

entrained mass (–)q density (kg m�3)s time (s)

Subscript0 start of flashB aqueous NaCl solution (brine)cal calculated value.drp droplete equilibriumf flash chamberfit fitting valuel liquidm integral mean value during flash duration timemax maximumr references saturationsc steam-carryingsp separatingstm steamtg tangent pointtp turning point between fast and gradual evaporation

stagev vacuum chamber

D. Zhang et al. / International Journal of Heat and Mass Transfer 79 (2014) 618–627 619

Our research team did comparative study on heat transfer proper-ties between static and circulatory flash of pure water [8–10] andfound that, first, waterfilm temperature evolution in static flashwas strongly analogy with that in classical model of semi-infinitebody after a temperature disturb on its surface had been imposed,thus error function was recruited to fit into NEF evolution in staticflash. Second, NEF at outlet of flash chamber in circulatory flashshared same variation laws with that of final equilibrium NEF instatic flash, depending on which a unified calculation model forboth flashes was set up initially. Third, considering that the wholebulk of water all took part in the flash, volumetric heat transfercoefficient was proposed to measure the intensity of boiling heattransfer for both flashes. Result suggested that, in circulatory flash,a peak value of volumetric heat transfer coefficient existed withincreasing horizontal velocity of waterfilm.

Mainly for its application in desalination, working fluid inresearch was gradually changed from pure water to aqueous NaClsolution. Gopalakrishna et al. [11] carried out static flash of aque-ous NaCl solution. Superheat ranged between 0.5 and 10 K, concen-tration of NaCl varied between 0 and 0.035 (mass fraction).According to experimental results, they proposed a formula forfinal evaporated mass. Miyatake et al. [12,13] investigated theinfluence of salt concentration of waterfilm on the bubble growthin stable pool boiling, and set up a simple calculation model. Liuet al. [14] did experiments on flash evaporation of aqueous NaCldroplet, and found vaporization rate could be minimized by higherconcentration or environment pressure. Our research team [15]also did static flash experiments with NaCl concentration enlargedinto 0–0.15 (mass fraction), superheat into 1.7–53.6 K. Results sug-gested that higher initial height or initial concentration of water-film weakened the intensity of boiling heat transfer. But highersuperheat just did oppositely. Due to the fact that the influenceof superheat and initial height of waterfilm on flash of aqueous

NaCl solution was same as that on flash of pure water, NEF evolu-tion of aqueous NaCl solution was also fitted by error function.

Although vaporization and steam-carrying effect takes placesimultaneously and together causes mass transfer during flash,research on steam-carrying effect seems rare. In our previousresearch, theoretical height drop of waterfilm was defined as thecalculated results from its temperature drop according to heat bal-ance. Results found that the height drop measured in experimentwas far greater than the theoretical height drop, suggesting thatsteam-carrying effect was ubiquitous in flash vaporization. Then,steam-carrying ratio was introduced as mass ratio of entrainedliquid and flash steam. Results suggested that this ratio increasedwith rising initial height or rising initial salt concentration ofwaterfilm, and a peak value existed in its evolution versus meanpressure difference between flash and vacuum chamber. Basedon force analysis of single droplet submerged in upward flowingsteam, a calculation model for steam-carrying effect in static flashwas set up [16].

In addition, there were also many works on industrial applica-tion of flash. Chung et al. [17] examined the performance of singlestage circulatory flash system. Miyatake et al. [18] and Jin et al.[19] also did researches on multi-stage flash (MSF). An improve-ment for custom MSF was proposed and analyzed by our researchteam [20].

Former works uncovered the basic mechanism of static flash,but limitations still existed. First, static flash in previous worksmainly took place freely; the temperature or height drop duringflash was out of control. But in order to study boiling heat transfer,steam-carrying effect of static flash at micro level, or to developcommercial application, controllable flash should be developedand its properties at different flash speeds should be examined.Second, boiling heat transfer and steam-carrying effect were twoimportant fields in research of flash, but former study focused

620 D. Zhang et al. / International Journal of Heat and Mass Transfer 79 (2014) 618–627

mainly on boiling heat transfer properties, seldom on steam-carry-ing effect, and research about this effect at different flash speedwas even less.

Our research team examined boiling heat transfer characteris-tics of static flash at different flash speed [21]. In this study, flashspeed was defined as the mean decreasing rate of NEF during fastevaporation stage. In experiments, different flash speeds were gen-erated by adding throttle orifice plate with different orifice diame-ters (5–80 mm) between flash and vacuum chamber. Resultssuggested that, first, shrinking orifice diameter from 80 to 5 mmreduced flash speed for about one or two orders of magnitudes.Second, initial salt concentration of waterfilm had nearly no obvi-ous influence on flash speed. Third, volumetric heat transfer coef-ficient just increased linearly with rising flash speed.

Now, this paper focus on the properties of steam-carrying effectat different flash speed and can be viewed as a continuation of Ref.[21]. Specifically, steam-carrying ratio under different orifice diam-eters (5–80 mm) of throttle orifice plate is measured, and itsdependence on flash speed and superheat are examined. Besides,the influences of steam-carrying effect on height drop of waterfilmand equilibrium salt concentration of waterfilm at different flashspeed are also studied. According to these results, an enhancedmodel for steam-carrying effect at different flash speed is set up.

2. Experimental system and uncertainty analysis

2.1. Experimental system

Research in this paper is based on the same experimental sys-tem (Fig. 1) and the same steps stated in our former works[16,21]. The experimental system includes high and low pressurepart. High pressure part contains heater and flash chamber. Flashchamber is a 0.20 � 0.20 � 0.50 m rectangular tank, and its frontand rear faces are made of tempered glass for observation. Low

(1). heater(2). flash chamber(3). electromagnetic valve(4). vacuum chamber(5). condenser(6). vacuum pump

(7). cooling wa(8). cooling wa(9). thermomet(10). barometer(11). pressure t(12). thermoco

Fig. 1. Experimental system for stati

pressure part includes vacuum chamber, vacuum pump and auxil-iary condensing system. Two parts are connected by electromag-netic valve with internal diameter is 80 mm. In order to generatedifferent flash speeds in experiment, four thin orifice plates withdifferent orifice diameters (5, 10, 20, 40 mm) are respectivelyinstalled at the inlet of electromagnetic valve (section A-A inFig. 1). Combined with the state without orifice plate, five differentflow areas are available.

In experiment, aqueous NaCl solution at certain concentrationwas first heated and then channeled into flash chamber untilreached required initial height of waterfilm. Meantime, auxiliarycondensing system and vacuum pump were started up to createrequired vacuum pressure in vacuum chamber. After preparationson both parts were finished, the electromagnetic valve was openedand flash took place.

During flash, the quickly decaying temperature of waterfilm,pressure of flash and vacuum chamber were real-timely measuredand stored. After flash, equilibrium height of waterfilm was mea-sured by a cathetometer fixed outside the front glass of flash cham-ber. The equilibrium salt concentration of waterfilm was measuredby float densimeter. The structure of each component and theinformation about the measurement equipment, method of dataprocessing had been clearly introduced in our previous works[16,21] and not repeated here.

2.2. Determination for steam-carrying ratio

Steam-carrying ratio is defined as the mass ratio of entrainedliquid to flash steam. The value of this ratio can be deduced fromheight drop of waterfilm (DH) and non-equilibrium fraction(NEF) that measured in experiment. Thus, definition of NEF shouldbe briefly reviewed first.

NEF is defined on basis of theoretical equilibrium temperature(TBse) and superheat. TBse is defined as saturation temperature

ter tankter pumper

ransduceruples

(13). filling valve(14). adjusting valve(15). drain valve(16). cathetometer(17). adjusting valve(18). high speed camera

c flash of aqueous NaCl solution.

D. Zhang et al. / International Journal of Heat and Mass Transfer 79 (2014) 618–627 621

under final equilibrium pressure of flash chamber added by boilingpoint elevation (h) of aqueous NaCl solution (Eq. (1)). It is viewedas the minimal value in theory that the temperature of waterfilmcan reach at the end of flash. Superheat is defined as the differencebetween initial temperature of waterfilm and TBse (Eq. (2)). Super-heat represents the maximum temperature drop during flash, orthe quantity of unstable energy contained in waterfilm. FinallyNEF is defined as the ratio of residual temperature difference ofwaterfilm with TBse to superheat (Eq. (3)). NEF is dimensionlesstemperature and represents completion degree of flash:

TBse ¼ TsðpfeÞ þ hðTBe; f meÞ ð1ÞDT ¼ TB0 � TBse ð2Þ

NEFðsÞ ¼ TBðsÞ � TBse

TB0 � TBse¼ TBðsÞ � TBse

DTð3Þ

Based on these concepts, the measurement formula for steam-carrying ratio could be deduced as following. According to massconservation, the height drop of waterfilm is attributed to bothvaporization and steam-carrying effect (Eq. (4)). Considering thatflash can be divided into fast evaporation stage and gradual evap-oration stage, and the temperature of waterfilm drops fast andsignificantly during former stage, thus, in this paper, the durationof fast evaporation stage is defined as flash duration time, andthe heat and mass transfer during flash is assumed to completelytake place in this stage (the definition of the turning point willbe introduced in detail in Section 3.1). Therefore, the total massof flash steam generated during flash can be deduced as Eq. (5)according to heat balance. Here and in following discussion, sub-script tp stands for the value at turning point from fast evaporationstage to gradual evaporation stage. Substituting Eq. (5) into Eq. (4)and neglecting the change of liquid density (ql) during flash, themass ratio of entrained liquid to flash steam, or the steam-carryingratio, is reached as Eq. (6), which is viewed as its measurement for-mula in this paper. The experimental result of K and its variationlaw will be discussed in detail in Section 3.4:

qlADH ¼ mstm þmsc ð4Þ

mstm ¼ qlAH0Jað1� NEFtpÞ; where Ja ¼ cpDTr

ð5Þ

K ¼ msc

mstm¼ DH

H0Jað1� NEFtpÞ� 1 ð6Þ

2.3. Uncertainty analysis

The experimental ranges of main parameters and the uncer-tainty analyses results for all directly and indirectly measured val-ues are all listed in Table. 1. The uncertainty analyses is carried outaccording to method of constant odds—product form proposed byMoffat [22].

Table 1Experimental range of main parameters and uncertainty analysis.

Parameter xx Experimental range Absolutely uncertainty dxx

T (�C) 46.5–132.4 0.2H (m) 0.10, 0.15, 0.20, 0.25, 0.30 5.0 � 10�4

fm 0, 0.05, 0.10, 0.15 5.0 � 10�4

s (s) 20–1000 0.0125p (MPa) 0.00868–0.213 1.13 � 10�3

DT (K) 2.0–43.8 0.2K – –C – –

a Pure water does not require concentration measurement.

3. Result and analysis

3.1. Calculation for flash speed

As shown in Fig. 2, flash can be divided into fast evaporationstage and gradual evaporation stage depending on the decreasingrate of waterfilm temperature [3]. In our former works [21], theturning point (stp) between the two stages is defined as the inter-section of TBse and the largest slope tangent along curve of TB (pointB in Fig. 2(a)). In order to simplify following calculation model forsteam-carrying effect, definition of this turning point is improvedby replacing curve of waterfilm temperature TB with curve of thedimensionless waterfilm temperature NEF. In other words, theintersection of horizontal line NEF = 0 and the largest slope tangentalong curve of NEF is defined as turning point (point B in Fig. 2(b))in this paper, and duration of fast evaporation stage [0,stp] isdefined as flash duration time.

Under the new definition, stp can be directly calculated from thefitting formula of NEF (Eq. (7)) proposed in our previous works[21]. The slope along NEF equals to its first derivative as Eq. (8).Let the second derivative of NEF equals to zero (Eq. (9)), locationof the tangent with largest slope (point A in Fig. 2(b)) along NEFcan be deduced as Eq. (10). Further, the turning point stp (point Bin Fig. 2(b)) can be expressed as Eq. (11). In the view of the fact thatNEF is dimensionless temperature, the essence of the two defini-tion of stp is equivalent. Fig. 2 also testifies that their value differ-ence is tiny.

NEFðsÞ ¼ erfH0

2

ffiffiffiffiffiffiffiffiffiffiqlcpl

ks

r !a2" #

ð7Þ

where k ¼ 1:106 DTH0

D2

� ��0:535expð�1:603f m0Þ, and a2 = 0.0011 +

0.3400lnDT + 0.0202D � 0.0002D2.

NEF 0ðsÞ ¼ 2ffiffiffiffipp abe�a2s2bsb�1 ð8Þ

where a ¼ H02

ffiffiffiffiffiffiffiqlcpl

k

q� �a2

and b ¼ � a22 :

NEF 00ðsÞ ¼ 0 ð9Þ

stg ¼b� 12a2b

� � 12b

ð10Þ

stp ¼ stg �NEFðstgÞNEF 0ðstgÞ

ð11Þ

Flash speed is defined as mean decreasing rate of NEF duringflash duration time of [0,stp] as Eq. (12). Flash speed can be directlycomputed out on basis of Eq. (7), (8), (11). Here and in followingcalculation, the reference temperature and reference concentrationare respectively defined as Eqs. (13), (14), thermo-properties data

Minimal measured value xxmin Maximal uncertainty dxx/xxmin

46.5 4.3 � 10�3

0.10 0.0050.05a 0.01020 6.25 � 10�4

9.13 � 10�3 0.1302 0.10– 0.008– 0.011

(a) Definition according to waterfilm temperature in Ref.[21].

(b) Definition according to NEF.

0 20 40 60 80 100 12086

87

88

89

90

91

92

93

94

τ / s

T B /

o C

A (τtg, TB,tg)

B (τtp, TBs)

C (τtp, TB,tp)

LST

FES GES

TBTBsΔT=5.9Kfm0=0.051

H0=0.3m

D=20mmτtp=19.66s

0 20 40 60 80 100 1200

0.2

0.4

0.6

0.8

1

τ / s

NEF

A (τtg, NEFtg)

B (τtp, 0)

C (τtp, NEFtp)

LST

FES GES

NEFexpNEFfit,Eq.(7)

ΔT=5.9Kfm0=0.051

H0=0.3m

D=20mmτtp=20.67s

Fig. 2. LST, largest slope tangent. FES, fast evaporation stage. GES, gradualevaporation stage. Improved definition of turning point between fast and gradualflash stages.

622 D. Zhang et al. / International Journal of Heat and Mass Transfer 79 (2014) 618–627

of aqueous NaCl solution are cited from Refs. [23,24]. Under thisdefinition, flash speed in current experimental range variesbetween 2.5 � 10�3 and 7.33 s�1:

FS ¼ 1� NEFtp

stpð12Þ

Tr ¼12

TB0 þ TBseð Þ ð13Þ

f mr ¼12

f m0 þ f með Þ ð14Þ

3.2. Enhanced calculation model for steam-carrying effect

Our former works [16] set up a calculation model for steam-carrying effect in static flash without throttling the flash steam.In order to enlarge its application range to static flash at differentflash speeds, the original model is improved as following.

Ref. [16] assumes the mechanism of steam-carrying effect isthat, during static flash, sudden vaporization immediately gener-ates many vapor bubbles in waterfilm. Their overflow and ruptureat steam–liquid interface make waterfilm severely roll and alsobump with inner walls of flash chamber, generating a large numberof liquid droplets that are sprayed out of waterfilm. Some of thedroplets drop back and some are entrained away from flash cham-ber by upward flowing steam. Fig. 1 repeats force analysis for sin-gle droplet submerged in flash steam. Upward flowing steamexerts upward drag force and buoyancy force against gravity. Ref.

[16] proposes that equilibrium of the three force indicates the big-gest droplet that can be hold up by steam at given speed, anddeduces the mass of maximum droplet as Eq. (15), which dependsmainly on steam speed:

mdrp;max ¼9p128

C3f

g3

qlq3stm

ql � qstmð Þ3u6

stm;m ð15Þ

Instead of deducing from pressure difference between flash andvacuum chamber by Bernoulli equation in [16], the mean steamspeed (ustm,m) in this paper is deduced according to energy balanceby averaging the mass of flash steam (Eq. (5)) into flash durationtime [0,stp] as Eq. (16):

ustm;m ¼mstm

qstmAstp¼ qlAH0 Jað1� NEFtpÞ

qstmAstp¼ H0

ql

qstmJa � FS ð16Þ

If theoretical maximum number of droplet that can be carriedby each unit mass of steam is N, the total mass of entrained liquidcan be expressed as Eq. (17), where n is the ratio of actuallyentrained mass to theoretical maximum entrained liquid. Consid-ering that flash takes place fiercely and fast, and the values of n,N, Cf cannot be measured in current experimental system or beestimated according basic theory. Thus, terms in the first parenthe-ses of Eq. (17) is absorbed in an intermediate variable, named assteam-carrying coefficient, as Eq. (18). This has two advantages,first, it simplifies the expression of entrained liquid. Second, thevalue of C can be deduced from experimental data (will be dis-cussed in Section 3.3), which is meaningful for the modeling.Besides, considering that the density of waterfilm (ql) is about3800 times larger than density of steam (qstm) in current experi-mental range, thus (ql � qstm) in Eq. (17) can be replaced by ql.Finally, the total mass of entrained liquid is greatly simplified asthat behind the third equal sign in Eq. (17). Further, the steam-car-rying ratio can be easily deduced as Eq. (19):

msc ¼ n � N �mdrp;maxmstm

¼ n � N � 9p128

C3f

g3

!� q7

l

ðql � qstmÞ3q3

stm

ðH0 � Ja � FSÞ6 �mstm

¼ C � q7l

q3l q

3stmðH0 � Ja � FSÞ6 �mstm ð17Þ

C ¼ n � N � 9p128

C3f

g3 ð18Þ

K ¼ msc

mstm¼ C � q4

l

q3stmðH0 � Ja � FSÞ6 ð19Þ

Compared with the model set up in Ref. [16], the new model hastwo improvements. First, new model approximately thinks that theheat and mass transfer in flash boiling completely take place in fastevaporation stage, rather than entire flash process. Second, themean speed of flash steam in this paper is calculated from energybalance. These two improvements successfully introduce flashspeed into the model, and simplify following discussion. Thisnew model is named ‘‘enhanced calculation model for steam-car-rying effect’’ in this paper.

3.3. Steam-carrying coefficient

Although steam-carrying coefficient cannot be directly mea-sured according to its definition in current experimental system,considering that the steam-carrying ratio (K) has already beenmeasured by Eq. (6) through experiments, this coefficient (C) canbe easily computed from the measured value of K, initial heightof waterfilm, flash speed as well as temperature of waterfilmaccording to Eq. (20), which is reshaped from Eq. (19):

5

10

15

20

25

30

35

K

1

23

1, D=80mm2, D=20mm3, D=10mm4, D=5mmH0=0.2m

fm0=0.05

Eq.(22)

D. Zhang et al. / International Journal of Heat and Mass Transfer 79 (2014) 618–627 623

C ¼ Kq3

stm

q4l

H0 � Ja � FSð Þ�6 ð20Þ

Fig. 3 depicts experimental result of C versus superheat. It sug-gests that C decreases with increasing superheat. But under thesame superheat, C increases significantly with rising initial heightof waterfilm or with shrinking orifice diameter, and slightly risingwith increasing initial salt concentration of waterfilm. According tothese variation laws, C is fitted as Eq. (21). In this formula, coeffi-cient b2 varies under different orifice diameters and is listed inTable. 2. Fig. 4 further displays that about 90.3% of the relativeerrors between fitting and experimental steam-carrying coefficientfall into the range of ±10%:

0 10 20 30 40 50-10

0

10

20

30

40

50

60

ΔT / K

lnC

/ kg

-1m

-3s6

1, D=80mm, H0=0.3m, f

m0=0.15

2, D=80mm, H0=0.3m, f

m0=0

3, D=80mm, H0=0.1m, f

m0=0.15

4, D=80mm, H0=0.1m, f

m0=0

5, D=5mm, H0=0.3m, f

m0=0.15

6, D=5mm, H0=0.3m, f

m0=0

7, D=5mm, H0=0.1m, f

m0=0.15

8, D=5mm, H0=0.1m, f

m0=0

Eq.(21), top-down are 1-8 respectively

Fig. 3. Steam-carrying coefficient versus superheat under different initialconditions.

Table 2Value of fitting coefficient b2 in Eq. (21) under different orificediameters.

D/mm b2

80 �4.2940 �5.5620 �6.1810 �6.21

5 �5.39

0 10 20 30-5

0

5

10

15

20

25

30

35

lnCexp / kg-1m-3s6

lnC

fit,

Eq.(2

1) /

kg-1

m-3

s6

10.0% →← -10.0%

90.3% in range of ±10.0%

Fig. 4. Relative error between fitting and experimental steam-carrying coefficient.

0 10 20 30 40 500

ΔT / K

4

Fig. 5. Steam-carrying ratio versus superheat under different orifice diameters.

ln Cfit ¼ b1 þ b2DT � 27:6204 expð�DT0:5Þ þ 10:3227 ln H0

þ 13:287f m0 ð21Þ

where b1 = 0.002D2�0.5043D + 62.083, b2 is listed in Table. 2.

3.4. Steam-carrying ratio

Fig. 5 displays steam-carrying ratio (K) versus superheat underdifferent orifice diameters. It suggests that a peak value of K existsversus superheat, but the peak value quickly drops with shrinkingorifice diameter. When diameter is reduced to 5 mm, the peakvalue is so unobvious that K almost increases linearly with risingsuperheat. This result can be attributed to steam speed which isthought as main driving force for steam-carrying effect. Whensuperheat is small, steam speed is too low to hold up big droplet,leading steam-carrying ratio to be smaller. But when superheat istoo larger, severely upward flowing steam entrains a lot of liquidthat congests at steam exit of flash chamber. It is difficult forentrained liquid to pass through and most of them drops back towaterfilm, making steam-carrying ratio is still small. Two extremestates suggests that at least a peak value exists versus superheat.With the shrinking of orifice diameter, the throttling effect slowsdown steam speed and makes its variation with superheat is nolonger severe, leading the peak value of steam-carrying rate toquickly drop and even to be unobvious when orifice is reducedto 5 mm. This result also indicates that throttling steam is an effec-tive way to suppress steam-carrying effect.

10-3 10-2 10-1 100 1010

10

20

30

40

50

60

70

80

FS / s-1

K

D=5mmD=10mm

D=20mm

D=40mm

D=80mm

H0=0.1m

H0=0.2m

H0=0.3m

Eq.(22)ΔT=15Kfm0=0.1

Fig. 6. Steam-carrying ratio versus flash speed under different initial heights ofwaterfilm.

10-2 10-10

5

10

15

20

25

30

35

40

45

FS / s-1

K

D=5mmD=10mm

D=20mm

D=40mm

D=80mmfm0=0

fm0=0.05

fm0=0.15

Eq.(22)ΔT=17KH0=0.2m

Fig. 7. Steam-carrying ratio versus flash speed under different initial salt concentrations of waterfilm.

624 D. Zhang et al. / International Journal of Heat and Mass Transfer 79 (2014) 618–627

Figs. 6 and 7 respectively plot steam-carrying ratio versus flashspeed under different initial height of waterfilm (H0) or under dif-ferent initial salt concentrations of waterfilm (fm0). Both figuressuggest that, first, K increases with flash speed. Second, underthe same flash speed, K increases with rising initial height ofwaterfilm or rising initial salt concentration of waterfilm. The firstresult can be explained by Eq. (16) that fast flash speed raisessteam speed, makes steam of unit mass entrain more large drop-lets, thus increasing steam-carrying ratio. The second result canbe explained by separating height (Hsp) as shown in Fig. 1. Separat-ing height is defined as difference between height of flash chamberand height of free surface of waterfilm. Hsp directly represents theelevation for droplets to be entrained out of flash chamber. In cur-rent experimental system, height of flash chamber is unchanged,and higher H0 reduces Hsp, making droplets more easier to be taken

Fig. 8. Flash process at

out of flash chamber, and thus increasing steam-carrying ratio. Ref.[16] compares a set of flash photos taken by high speed camera. Itconcludes that during flash, vapor bubble accumulates at steam-liquid interface to form a layer, and height of the layer increaseswith rising fm0. This phenomenon also reduces separating heightand correspondingly increases steam-carrying ratio. Besides,Fig. 6 also indicates that the adjustable range of K acquired bychanging orifice diameter enlarges with increasing initial heightof waterfilm.

Substituting above fitting formula of C (Eq. (21)) into Eq. (19),the calculation formula for steam-carrying ratio can be expressedas Eq. (22):

Kcal ¼ Cfit �q4

l

q3stm

H0 � Ja � FSð Þ6 ð22Þ

The solid lines in Figs. 5–7 indicates that the calculated steam-carrying ratio matches well with experimental result in most cases.Large deviation only exists at fast flash speed (Figs. 6 and 7). Thereason can be explained by Fig. 8, which displays a set of photostaken by high speed camera during a static flash at flash speed of2.36 s�1. At this high flash speed, the rapidly generated flash steamhas no time to diffuse out the bulk of waterfilm, but fully blendswith liquid to forms foam-like mixture and gushes out flash cham-ber. Apparently, the steam-carrying mechanism now is far differ-ent from that assumed in our model that some droplets aredirectly entrained away by upward flowing flash steam. The mech-anism deviation leads to calculation error at fast flash speed. Fig. 9further indicates in current experimental range, 90.3% of the rela-tive errors between calculated and experimental steam-carryingratio fall into the range of ±50%.

3.5. Height drop of waterfilm

During flash, height drop of waterfilm is an important change(For example, height of waterfilm drops from 0.102 to 0.039 m in

high flash speed.

0 20 40 60 800

10

20

30

40

50

60

70

80

Kexp

Kca

l, Eq

.(22) 50.0% →

← -50.0%

90.3% in range of ±50.0%

Fig. 9. Relative error between calculated and experimental steam-carrying ratio.

10-2 10-1

10-2

10-1

100

FS / s-1

Δ H /

m

1

1

2

2

3

3

D=5mm D=10mm

D=20mm

D=40mm

D=80mm

1, H0=0.20m

2, H0=0.25m

3, H0=0.30m

Eq.(24)Eq.(25)ΔT=25Kfm0=0.1

Fig. 10. Height drop of waterfilm versus flash speed under different initial saltconcentrations of waterfilm.

D. Zhang et al. / International Journal of Heat and Mass Transfer 79 (2014) 618–627 625

Fig. 8). The height drop is caused by both vaporization and steam-carrying effect. According to our model, the mass of entrainedliquid can be expressed as Eq. (23). Therefore, height drop ofwaterfilm can be expressed as Eq. (24). If think this height dropis caused only by vaporization, it can be expressed as Eq. (25):

0 0.1 0.2 0.30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

ΔHexp / m

Δ Hca

l, Eq.

(24)

/ m

50.0% →

← -50.0%

96.6% in range of ±50.0%

Fig. 11. Relative error between calculated and experimental height drop ofwaterfilm.

msc ¼ m0Jað1� NEFtpÞKcal ð23Þ

DHcal ¼mstm þmsc

qlA¼ H0Jað1� NEFtpÞð1þ KcalÞ ð24Þ

DHcal ¼mstm

qlA¼ H0 Jað1� NEFtpÞ ð25Þ

Experimental results of height drop of waterfilm and the calcu-lation result with and without consider steam-carrying effect arecompared in Fig. 10. It suggests that, height drop of waterfilmincreases fast with the accelerating of flash speed, and at the sameflash speed, the height drop increase with rising initial height ofwaterfilm. These results are consistent with former variation lawsof steam-carrying ratio. Fig. 10 also indicates that the calculatedresult with consider steam-carrying effect (Eq. (24)) matches wellwith experimental results. But the calculated drops that consideronly vaporization (Eq. (25)) just increases slightly with flash speed,and are smaller than experimental height drop for about one orderof magnitude. This result testifies again that steam-carrying effectcannot be neglected, but plays a major role for the mass transferduring flash.

Fig. 11 further displays that 96.6% of the relative errors betweencalculated (Eq. (24)) and experimental height drop fall into therange of ±50%.

3.6. Equilibrium salt concentration of waterfilm

The variation of salt concentration of waterfilm is also animportant change during flash. Equilibrium salt concentration ofwaterfilm (fme) is directly measured in experiment. On basis ofour model, fme can also be deduced according to water balance(Eq. (26)) and salt balance (Eq. (27)). Substituting Eq. (5) and Eq.(23) into these two equation, the calculation formula for equilib-rium salt concentration of waterfilm is solved as Eq. (28):

m0 ¼ me þmstm þmsc ð26Þm0 f m0 ¼ mef me þmstm � 0þmsc f m0 ð27Þ

f me;cal ¼m0f m0

m0 �mstm �msc¼ 1� Jað1� NEFtpÞKcal

1� Jað1� NEFtpÞð1þ KcalÞf m0 ð28Þ

The experimental and calculated fme versus flash speed (FS) arecompared in Fig. 12. It indicates that fme has nearly nothing to dowith increasing flash speed, only slightly increases when FS is fas-ter than 0.2 s�1. This result can be explained by Eq. (29) which isreshaped from Eq. (28). Take the state fm0 = 0.15 in Fig. 12 forexample, Ja is about 0.037 and NEFtp is 0.28. These two parametershave nearly nothing to do with flash speed according to our formerworks [21]. The reciprocal of Ja(1 � NEFtp) is 37.6 and is much lar-ger than (1 + K) when flash speed is slow. But according to abovevariation law, K increases significantly with rising flash speedand is as large as 24.7 when FS is faster than 0.2 s�1, which is con-siderable compared with reciprocal of Ja(1 � NEFtp), leading fme

slightly increases from this moment:

f me;cal ¼ 1þ 11

Jað1�NEFtpÞ � ð1þ KcalÞ

" #f m0 ð29Þ

Essentially, vaporization and steam-carrying effect take placesimultaneously during flash. Vaporization separates water fromaqueous NaCl solution and makes the remain solution morethicker. While steam-carrying effect entrains a lot of solution with-out separating, but significantly reduces the mass of remain solu-tion, makes residual salt dissolve in even less solvent, indirectlyincreases fme, but this strengthen effect is weak. This result indi-cates that although steam-carrying effect enhances mass transferduring flash, it does not separate water from aqueous NaCl solu-tion, or improve the separation efficiency during flash.

10-3 10-2 10-1

0.05

0.1

0.15

0.2

0.25

FS / s-1

f me

D=5mmD=10mm

D=20mmD=40mm

D=80mm

fm0=0.05

fm0=0.1

fm0=0.15Eq.(28)ΔT=25KH0=0.25m

Fig. 12. Equilibrium salt concentration of waterfilm versus flash speed underdifferent initial salt concentrations of waterfilm.

0 0.05 0.1 0.150

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

fme,exp

f me,

cal, E

q.(2

8) 10.0% →← -10.0%

94.4% in range of ±10.0%

Fig. 13. Relative error between calculated and experimental equilibrium saltconcentration of waterfilm.

626 D. Zhang et al. / International Journal of Heat and Mass Transfer 79 (2014) 618–627

Besides, the solid lines in Fig. 12 suggest that the calculated fme

matches well with experimental result. Its relative error comparedwith experimental fme are displayed in Fig. 13, indicating that94.4% of the relative errors fall into the range of ±10%.

4. Conclusion

Experimental study on steam-carrying effect at different flashspeed was carried out on basis of experimental system stated inour former works [16,21]. Flash speed was defined as meandecreasing rate of NEF during fast evaporation stage. In experi-ment, different flash speeds were generated by installing thin ori-fice plates with different diameters (5–80 mm) between flash andvacuum chamber. The experimental range of main parameterswere listed in Table. 1.

Steam-carrying ratio was defined as the mass ratio of entrainedliquid to flash steam. Results suggested that, first, a peak value ofsteam-carrying ratio existed with increasing superheat, but thepeak value quickly dropped with shrinking orifice diameter.Second, steam-carrying ratio quickly increased with acceleratingof flash speed, and at the same flash speed, this ratio also increasedwith rising initial height or rising initial salt concentration ofwaterfilm. Third, the adjustable range of steam-carrying ratioachieved through changing orifice diameter enlarged with theincrease of initial height of waterfilm.

Height drop of waterfilm was examined and was found thatsteam-carrying effect played a major role for this drop. Corre-sponding to the variation law of steam-carrying ratio, height dropof waterfilm also significantly increased with rising flash speed, orwith rising initial height of waterfilm under same flash speed.

Equilibrium salt concentration of waterfilm had nearly nothingto do with flash speed. This result indicated that although steam-carrying effect entrained a lot of liquid during flash, it cannot sep-arate water from aqueous NaCl solution, thus hardly affected equi-librium salt concentration of waterfilm.

At last, an enhanced calculation model for steam-carrying effectduring static flash at different flash speed was set up on basis ofNEF fitting formula proposed in [21] and the model of steam-carry-ing effect without throttling set up in [16]. According to thisenhanced model, steam-carrying ratio, height drop and equilib-rium salt concentration of waterfilm could be computed withinacceptable error range and their dependences on flash speed andother initial conditions could also be analyzed. Larger calculationerror for steam-carrying ratio only appeared at faster flash speed,because the mechanism for steam-carrying at fast flash speedwas far different from that assumed in our model.

Now, improvement for our experimental system is being car-ried out and the mechanism of steam-carrying effect at fast flashspeed is being studied.

Conflict of interest

Neither the entire paper nor any part of its content has beenpublished or has been accepted elsewhere. Also, it is not beingsubmitted to any other journal. We will appreciate your favorableconsideration.

Acknowledgments

This work is supported by National Natural Science Foundationof China (51306148/51125027) and the Fundamental ResearchFunds for the Central Universities.

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