John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook (776116), страница 67
Текст из файла (страница 67)
They grow at the heated surface and condense verysuddenly when their tops encounter the still-cold water above them.This cavitation collapse is accompanied by a small “ping” or “click,”over and over, as the process is repeated at a fairly high frequency.• As the temperature of the liquid bulk rises, the singing is increasingly muted. You may then look in the pan and see a numberof points on the bottom where a feathery blur appears to be affixed. These blurred images are bubble columns emanating scoresof bubbles per second. The bubbles in these columns condensecompletely at some distance above the surface.
Notice that the airbubbles are all gradually being swept away.• The “singing” finally gives way to a full rolling boil, accompaniedby a gentle burbling sound. Bubbles no longer condense but nowreach the surface, where they break.• A full rolling-boil process, in which the liquid bulk is saturated, isa kind of isolated-bubble process, as plotted in Fig. 9.2.
No kitchenstove supplies energy fast enough to boil water in the slugs-andcolumns regime. You might, therefore, reflect on the relative intensity of the slugs-and-columns process.Experiment 9.2Repeat Experiment 9.1 with a glass beaker instead of a kitchen pan.Place a strobe light, blinking about 6 to 10 times per second, behind thebeaker with a piece of frosted glass or tissue paper between it and thebeaker.
You can now see the evolution of bubble columns from the firstsinging mode up to the rolling boil. You will also be able to see naturalconvection in the refraction of the light before boiling begins.463464Heat transfer in boiling and other phase-change configurations§9.2Figure 9.4 Enlarged sketch of a typical metal surface.9.2Nucleate boilingInception of boilingFigure 9.4 shows a highly enlarged sketch of a heater surface. Most metalfinishing operations score tiny grooves on the surface, but they also typically involve some chattering or bouncing action, which hammers smallholes into the surface.
When a surface is wetted, liquid is prevented bysurface tension from entering these holes, so small gas or vapor pocketsare formed. These little pockets are the sites at which bubble nucleationoccurs.To see why vapor pockets serve as nucleation sites, consider Fig.
9.5.Here we see the problem in highly idealized form. Suppose that a spherical bubble of pure saturated steam is at equilibrium with an infinitesuperheated liquid. To determine the size of such a bubble, we imposethe conditions of mechanical and thermal equilibrium.The bubble will be in mechanical equilibrium when the pressure difference between the inside and the outside of the bubble is balanced bythe forces of surface tension, σ , as indicated in the cutaway sketch inFig. 9.5.
Since thermal equilibrium requires that the temperature mustbe the same inside and outside the bubble, and since the vapor insidemust be saturated at Tsup because it is in contact with its liquid, theforce balance takes the form2σRb = psat at Tsup − pambient(9.1)The p–v diagram in Fig. 9.5 shows the state points of the internalvapor and external liquid for a bubble at equilibrium. Notice that theexternal liquid is superheated to (Tsup − Tsat ) K above its boiling point atthe ambient pressure; but the vapor inside, being held at just the rightelevated pressure by surface tension, is just saturated.Nucleate boiling§9.2Figure 9.5 The conditions required for simultaneous mechanical and thermal equilibrium of a vapor bubble.Physical Digression 9.1The surface tension of water in contact with its vapor is given withgreat accuracy by [9.3]:Tsat 1.256TsatmNσwater = 235.8 1 −(9.2a)1 − 0.625 1 −TcTcmwhere both Tsat and the thermodynamical critical temperature, Tc =647.096 K, are expressed in K.
The units of σ are millinewtons (mN)per meter. Table 9.1 gives additional values of σ for several substances.Equation 9.2a is a specialized refinement of a simple, but quite accurate and widely-used, semi-empirical equation for correlating surface465Table 9.1 Surface tension of various substances from thecollection of Jasper [9.4]a and other sources.SubstanceAcetoneAmmoniaAnilineBenzeneButyl alcoholCarbon tetrachlorideCyclohexanolEthyl alcoholEthylene glycolHydrogenIsopropyl alcoholMercuryMethaneMethyl alcoholNaphthaleneNicotineNitrogenOctaneOxygenPentaneTolueneWaterTemperatureRange (◦ C)25 to 50−70−60−50−4015 to 901030507010 to 10015 to 10520 to 10010 to 10020 to 140−258−255−25310 to 1005 to 2009010011510 to 60100 to 200−40 to 90−195 to −18310 to 120−202 to −18410 to 3010 to 10010 to 100σ (mN/m)σ = a − bT (◦ C)a (mN/m)b (mN/m·◦ C)26.260.11244.830.108527.1829.4935.3324.0550.210.089830.12240.09660.08320.08942.3940.2537.9135.3830.2127.5624.9622.402.802.291.9522.90490.60.07890.204924.0042.8441.0726.4223.52−33.7218.2530.9075.830.07730.11070.11120.22650.09509−0.25610.110210.11890.147718.87716.32812.371nSubstanceCarbon dioxideCFC-12 (R12) [9.5]HCFC-22 (R22) [9.5]TemperatureRange (◦ C)−56 to 31σ = σo [1 − T (K)/Tc ]σo (mN/m)75.00Tc (K)n304.261.25−148 to 11256.52385.011.27−158 to 9661.23369.321.23HFC-134a (R134a) [9.6]−30 to 10159.69374.181.266Propane [9.7]−173 to 9653.13369.851.242aThe function σ = σ (T ) is not really linear, but Jasper was able to linearize it overmodest ranges of temperature [e.g., compare the water equation above with eqn.
(9.2a)].466Nucleate boiling§9.2467tension: σ = σo 1 − Tsat Tc11/9(9.2b)We include correlating equations of this form for CO2 , propane, and somerefrigerants at the bottom of Table 9.1. Equations of this general formare discussed in Reference [9.8].It is easy to see that the equilibrium bubble, whose radius is describedby eqn. (9.1), is unstable. If its radius is less than this value, surfacetension will overbalance [psat (Tsup ) − pambient ]. Thus, vapor inside willcondense at this higher pressure and the bubble will collapse.
If thebubble radius is slightly larger than the equation specifies, liquid at theinterface will evaporate and the bubble will begin to grow.Thus, as the heater surface temperature is increased, higher and highervalues of [psat (Tsup )−pambient ] will result and the equilibrium radius, Rb ,will decrease in accordance with eqn. (9.1). It follows that smaller andsmaller vapor pockets will be triggered into active bubble growth as thetemperature is increased. As an approximation, we can use eqn. (9.1)to specify the radius of those vapor pockets that become active nucleation sites.
More accurate estimates can be made using Hsu’s [9.9] bubble inception theory, the subsequent work by Rohsenow and others (see,e.g., [9.10]), or the still more recent technical literature.Example 9.1Estimate the approximate size of active nucleation sites in water at1 atm on a wall superheated by 8 K and by 16 K. This is roughly inthe regime of isolated bubbles indicated in Fig. 9.2.Solution. psat = 1.203 × 105 N/m2 at 108◦ C and 1.769 × 105 N/m2at 116◦ C, and σ is given as 57.36 mN/m at Tsat = 108◦ C and as55.78 mN/m at Tsat = 116◦ C by eqn.
(9.2a). Then, at 108◦ C, Rb fromeqn. (9.1) is2(57.36 × 10−3 ) N/m1.203 × 105 − 1.013 × 105 N/m2Rb = and similarly for 116◦ C, so the radius of active nucleation sites is onthe order ofRb = 0.0060 mm at T = 108◦ Cor0.0015 mm at 116◦ C468Heat transfer in boiling and other phase-change configurations§9.2This means that active nucleation sites would be holes with diametersvery roughly on the order of magnitude of 0.005 mm or 5µm—at leaston the heater represented by Fig. 9.2. That is within the range ofroughness of commercially finished surfaces.Region of isolated bubblesThe mechanism of heat transfer enhancement in the isolated bubbleregime was hotly argued in the years following World War II. A few conclusions have emerged from that debate, and we shall attempt to identifythem.
There is little doubt that bubbles act in some way as small pumpsthat keep replacing liquid heated at the wall with cool liquid. The question is that of specifying the correct mechanism. Figure 9.6 shows theway bubbles probably act to remove hot liquid from the wall and introduce cold liquid to be heated.It is apparent that the number of active nucleation sites generatingbubbles will strongly influence q. On the basis of his experiments, Yamagata showed in 1955 (see, e.g., [9.11]) thatq ∝ ∆T a nb(9.3)where ∆T ≡ Tw − Tsat and n is the site density or number of active sitesper square meter. A great deal of subsequent work has been done tofix the constant of proportionality and the constant exponents, a and b.1The exponents turn out to be approximately a = 1.2 and b = 3 .The problem with eqn.
(9.3) is that it introduces what engineers calla nuisance variable. A nuisance variable is one that varies from systemto system and cannot easily be evaluated—the site density, n, in thiscase. Normally, n increases with ∆T in some way, but how? If all siteswere identical in size, all sites would be activated simultaneously, and qwould be a discontinuous function of ∆T . When the sites have a typicaldistribution of sizes, n (and hence q) can increase very strongly with ∆T .It is a lucky fact that for a large class of factory-finished materials, nvaries approximately as ∆T 5 or 6 , so q varies roughly as ∆T 3 .
This hasmade it possible for various authors to correlate q approximately for alarge variety of materials. One of the first and most useful correlationsfor nucleate boiling was that of Rohsenow [9.12] in 1952. It is0.332cp (Tw − Tsat )σq = Csf(9.4)µhfg g ρf − ρghfg Prs§9.2Nucleate boilingA bubble growing and departing in saturated liquid.The bubble grows, absorbing heat from thesuperheated liquid on its periphery. As it leaves, itentrains cold liquid onto the plate which then warmsup until nucleation occurs and the cycle repeats.469A bubble growing in subcooled liquid.When the bubble protrudes into coldliquid, steam can condense on the topwhile evaporation continues on thebottom.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
