1、478 2010 ASHRAEABSTRACTIn this paper, an attempt has been made to document theliterature on metastability, a phenomenon associated withboiling of liquids. The available correlations for the predictionof metastability have been presented and their range of appli-cations has also been discussed. In a
2、capillary tube, the meta-stability significantly influences the refrigerant mass flow rate.A comparison of Heurta et al. (2007) and Li et al. (1990) stud-ies on the metastable flow in adiabatic capillary tubes has beenmade. However, the only study on the metastable flow throughdiabatic capillary tub
3、es was conducted by Chen and Lin(2001). In the end, a simplified mathematical model based onthe previous works has also been presented to give the readersan insight into the numerical design of adiabatic capillarytubes, considering the phenomenon of metastability.INTRODUCTIONThe tendency of a fluid
4、to stay in its liquid state even if thefluid pressure falls below its saturation pressure is termed asmetastability. This is a non-equilibrium state of the fluid inwhich the liquid exists in a superheated state. Thus, thephenomenon of metastability always exists whenever a fluidundergoes a transitio
5、n from liquid phase to vapor phase. Thephenomenon of superheating of liquid above the saturationtemperature had been mainly investigated for the cases of crit-ical efflux in the flow boiling and of the superheating of awater bubble in a higher-boiling liquid. However, the presentdiscussion has been
6、limited to the metastability inside a capil-lary tube only, an expansion device used in the low capacityvapor compression refrigeration systems. The performance ofa refrigeration system greatly depends on the appropriateselection of the capillary tube size (bore and length) for a givenset of input c
7、onditions. To achieve the desired pressure dropfrom a capillary tube, the length of the capillary tube for givencapillary tube diameter is to be determined. The refrigerantwhile passing though the capillary tube undergoes a phasechange from liquid state to vapor state. Thus, the entire capil-lary tu
8、be can be divided in two three distinct regions- singlephase subcooled liquid region, the metastable region and thetwo-phase region. To determine the length of capillary tube,the length of each of the three regions has to be evaluated. Theaccurate prediction of metastable length is a must for effect
9、ivedesigning of capillary tube for a given application. Hence, thestudy of the phenomenon of metastability becomes importantas it helps to determine the initial conditions of the flashingprocess.The objective of the present work is to not only highlightthe significance of the metastable flow in a ca
10、pillary tube butalso to discuss the available correlations for the prediction ofunderpressure of vaporization in a capillary tube. Further-more, this paper presents a critical review of the metastableflow in a capillary tube.THEORYWhen a fluid is depressurized, it passes from thesubcooled liquid sta
11、te to a superheated liquid state. As thepressure of fluid reaches Pvwell below its saturation pressurePsthe flashing of liquid into vapour takes place. Ideally, thevaporization must start when the pressure of the fluid reachesthe saturation pressure, instead the fluid continues to be inliquid state,
12、 or, more appropriately in a superheated liquidstate. In other words, the vaporization is delayed. This pres-sure difference (Ps Pv) is known as underpressure of vapor-ization or pressure undershoot or delay of vaporization. TheMetastable Flow inside Capillary Tubes: A Critical ReviewMohd. Kaleem Kh
13、an, PhDMohd. Kaleem Khan is an assistant professor in the Department of Mechanical Engineering, Indian Institute of Technology Patna, PatliputraColony.OR-10-050 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 20
14、10, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. ASHRAE Transactions 479underpressure of vaporization is the measure of metastability.The reason for the exist
15、ence of this non-equilibrium metasta-ble state may be attributed to turbulent fluctuations of hotdepressurizing fluid. Moreover, a finite amount of superheat isrequired for the formation of first bubble to initiate the vapor-ization process. Figure 1 depicts the process of depressuriza-tion. From th
16、e initial state, the fluid undergoes isentropicprocess, almost coincident with the isothermal process in thesubcooled liquid region. As the liquid pressure falls below thesaturation pressure, Ps, corresponding to initial temperature Ti,nucleation process starts to occur. Faster the rate of depressur
17、-ization (dP/dt), higher will be the underpressure of vaporiza-tion and, flashing takes place with a greater violence. (Alamgirand Lienhard 1981).Now, to quantify the phenomenon of metastability, anucleation theory based on statistical mechanics was devel-oped by Volmer and Weber (1926), Becker and
18、Doring (1935),Zeldovich (1943), Kagan (1960), Blander and Katz (1973).The nucleation theory can be grouped under two categories:homogeneous nucleation and heterogeneous nucleation. Table1 presents the salient features of either types of nucleation.As described in Table 1, the homogeneous nucleationr
19、equires special conditions for its onset. Thus, in almost allpractical applications the heterogeneous nucleation theory isapplied to determine the underpressure of vaporization.However, irrespective of the types of nucleation, the onset ofbubble nucleus depends upon amount of superheated liquidand t
20、he heat capacity of the container. The effects of prematurenucleation sites inherent on contacting surface can be elimi-nated either by superheating liquid droplet in an immiscibleliquid of high boiling point or by heating the contactingsurface with the test liquid rapidly so that the heat transfer
21、tothe liquid exceeds the latent heat of vaporization of the liquid(known as pulse heating method with fine platinum wires) asdescribed by Skripov (1974).Alamgir and Lienhard (1981) correlated the underpres-sure of vaporization of hot water with the system variables andproposed the following correlat
22、ion based on heterogeneousnucleation theory:(1)From the above relationship they suggested that the GibbsNumber for nucleation in water during depressurization is about28.2 5.8. Alamgir and Lienhard (1981) correlation has beenuseful in the design of commercially finished pressure vesselsand tubing. T
23、he underpressure of vaporization predicted fromthe above correlation lies in 10.4% error band. The above cor-relation was established in the ranges: 0.62 (Ti/Tcrit) 0.935and 0.004 Matm/s (dP/dt) 1.803 Matm/s.The rate of depressurization inside a closed conduit orpipe may be computed using the follow
24、ing relationship:(2)Hence, the rate of depressurization is the product of thefluid velocity inside the pipe and the pressure drop along thepipe length.Lee et al. (2003) have achieved the quasi-homogeneousnucleation of R-123 on a small spherical heater in micro-gravity. They adopted basic homogeneous
25、 nucleation theoryFigure 1 The depressurization process on P-v diagram.Table 1. Difference Between Homogeneous and Heterogeneous NucleationS.N. Homogeneous Nucleation Heterogeneous Nucleation1 This type of nucleation occurs when the surface in contact of the liquid is smooth and liquid is free from
26、pre-existing gases or vapors.Occurs when the surface in contact of liquid contains cavities. A less energy is required to form a bubble nucleus as the cavities may have gases or vapors present.2. There is no contact between the liquid and gas phases. Further, the liquid has zero contact angle with a
27、ll the surfacesOccurs at the interface between the liquid and another phase it contacts.3. Only internal parameters of liquid affect the barrier are the surface tension, the degree of superheat, and the temperature.The barrier is affected by not only internal parameters of liquid but also the materi
28、al properties such as rough-ness and geometry of the container.PsPv()kBTs1.5-0.252TiTcrit()13.73114dP dt()0.8+1 ffg()-=dPdt-dPdz-dzdt- VdPdz-= 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part
29、 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. 480 ASHRAE Transactionsrather than heterogeneous nucleation theory to explain theoccurrence of nucleation near the smooth surfa
30、ce of solidheater. They developed an analytical model, which solved theone-dimensional boundary value transient heat conductionproblem in spherical coordinates. The objective was to deter-mine the behavior of nucleation on a smooth approximatelyspherical solid heater. In this case, the heat flux and
31、 steeptemperature gradient at the surface might have been the causeof bubble nucleation.METASTABLE FLOW IN CAPILLARY TUBESThis section has been divided into two parts: First partcomprising of literature on metastability in adiabatic capil-lary tubes and second part contains literature on diabaticcap
32、illary tubes. The studies have been presented in a chrono-logical order in tabular as well as descriptive forms.Despite nearly six decades long research in adiabaticcapillary tubes, the performance of the capillary tubes are notso accurate simply because of the inability to locate the exactposition
33、of flash point in a capillary tube. The refrigerant massflow rate through a capillary tube greatly depends upon thepoint of inception of vaporization (flash point). The point ofvaporization could only be located if the exact metastableliquid length is known. The metastable liquid length, in turn,dep
34、ends upon the delay of vaporization. If the exact positionof flashpoint is not known the exact lengths of the single-phase and two-phase regions of the capillary tube could not bepredicted. The refrigerant mass flow rate will be more if thelength of single phase region is more and vice-versa. This i
35、sdue to the fact the liquid phase offers lesser resistance to theflow in comparison to the two-phase liquid vapor mixture.This is the main reason why the capillary tubes performanceprediction is not so accurate regardless of volumes of papersavailable in this area, containing both experimental andnu
36、merical models.Recently, Khan et al. (2009) have presented comprehen-sive review on the capillary tubes. They classified the availableliterature on the capillary tubes into experimental and numer-ical investigations of adiabatic and diabatic capillary tubes.The work on coiled capillary tubes have al
37、so been mentionedand elaborated. Further, they discussed the metastable flow incapillary tubes, albeit, not in details. Therefore, in the presentpaper, the emphasis is solely on the literature comprisingmetastable flow in capillary tubes.Having known the importance of metastability, it is nowincreas
38、ingly important to explore the available literature onthe metastable flow especially through capillary tubes. In thepresent work, a review of literature has been carried out forthe metastable flow of different refrigerants through adiabaticcapillary tubes in Table 2. Metastability in the flow throug
39、hthe adiabatic capillary tube was, probably, first observed anddiscussed by Cooper et al. (1957). Later on, Mikol (1963)confirmed the presence of metastable region in the capillarytube. These studies were conducted on R-22 and metastableregion was visually observed in the glass capillary tube. Theye
40、stablished that the location of point of inception is fixed andthat it moves in discrete steps rather than in a continuousfashion as operating parameters are varied. Koizumi andYokoyama (1980) also established the presence of this non-equilibrium region in the adiabatic capillary tube. In addition,t
41、hey measured pressure and temperature along the capillarytube length. A simplified numerical model, based on homog-enous two-phase flow model, was also developed to computethe length of the capillary tube. However, these studies did notquantify metastability in the form of some empirical correla-tio
42、n. A point must be noted at this stage that carrying outexperiments on the glass capillary tube cannot be comparedwith those on the actual copper drawn capillary tubes. This isdue to the fact that the internal surface of the glass capillarytube is highly smooth and does not contain irregularities in
43、general. Thus, the nucleation in glass capillary tube will be ofhomogeneous nature whereas in copper capillary tube nucle-ation is of heterogeneous nature. Because of near absence ofcavities on the glass capillary tube surface may cause a furtherdelay the vaporization process in the downstream direc
44、tion.Therefore, the length of metastable liquid region may be morethan that in actual capillary tube for the same operatingconditions.Kuijpers and Janssen (1983) tried to correlate degree ofsuperheat with capillary tube inlet pressure, inlet subcoolingfor R-12 in an adiabatic capillary tube. However
45、, this attemptwas not so successful. Further, Keuhl and Goldschmidt(1990) touched various aspects like metastability, effect ofcoiling etc. on the mass flow rate of R-22 through adiabaticcapillary tubes. Keuhl and Goldschmidt (1991) also devel-oped a numerical model to simulate the test results. An
46、aver-age value for the underpressure pressure was calculated,which helped in good agreement of the simulation results tothose with test results.Meyer and Dunn (1998) carried out a detailed investiga-tion on the metastable flow through adiabatic straight capil-lary tube. Further, they discovered the
47、hysteresis effect in themeasured mass flow rate with respect to direction of change ininlet subcooling (increasing/decreasing). The experimentalresults revealed that the mass flow rate at a given state pointcorresponding to decreasing inlet subcooling is higher thanthat corresponding to increasing i
48、nlet subcooling. They foundthat as inlet subcooling decreased, the flash point may hangup on the nucleation sites resulted in an elongation of meta-stable region. Consequently, a higher mass flow rate wascaused. As for the increasing inlet subcooling, the mass flowrate found to be lower due to vary
49、small or non-existent meta-stable region.A well established correlation for the prediction of under-pressure of vaporization in an adiabatic capillary tube wasdeveloped by Chen et al. (1990). This semi-empirical corre-lation was based on the heterogeneous nucleation theory andis as follows: 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 20
