sify the process of heat transfer as compared to any homogeneous liquid in the emulsion composition. The effect of considerable superheating of an emul.
ISSN 0018151X, High Temperature, 2011, Vol. 49, No. 1, pp. 143–146. © Pleiades Publishing, Ltd., 2011. Original Russian Text © A.K. Rozentsvaig, Ch.S. Strashinskii, 2011, published in Teplofizika Vysokikh Temperatur, 2011, Vol. 49, No. 1, pp. 139–142.
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Hydrodynamic Aspects of Boiling Up of a Disperse Phase in a Homogeneous Turbulent Flow of an Emulsion A. K. Rozentsvaig, and Ch. S. Strashinskii Kama State Academy of Engineering and Economics (INEKA), Naberezhnye Chelny, 423810 Russia Received July 21, 2008
DOI: 10.1134/S0018151X11010172
RESONANCE MECHANISM OF THE INITIATED BOILING UP
INTRODUCTION Emulsions of organosilicon liquids with an aque ous disperse phase are widely used for cooling of cut ting tools in the process of thermal treatment of met als [1, 2]. It turned out that they substantially inten sify the process of heat transfer as compared to any homogeneous liquid in the emulsion composition. The effect of considerable superheating of an emul sion was experimentally revealed in these works and then studied. The complexity of this phenomenon did not allow the authors to completely present all results of the experiments in accordance with a qual itative and quantitative explanation of the observed effect of the time delay in the boiling that they pro posed. In the same studies [1, 2], such factors of nucle ation as bubbles of the dissolved gas (air), solid microscopic particles, and surfaceactive com pounds was considered. Such an explanation of the nucleation does not take into account a series of important hydrodynamic factors. It is known that, in both turbulent and laminar motion modes, the dis persephase drops can collide, deform, and be destroyed by the dynamic and viscous forces of the flow of the emulsion [3]. The dynamic nature of the turbulent pulsations of pressure and velocity of a continuous medium can be due to not only the deformation of dispersed drops of liquid and vapor bubbles but also the formation of internal local areas with “negative” pressure able to initiate the nucleation of vapor bubbles [4]. For this reason, it is necessary to supplement the factors ini tiating the boiling of the dispersephase drops with those related to their deformation and fragmentation in the emulsion. Under conditions of resonance enhancement by the disperse phase, the energy of the turbulent flow can be sufficient for stable formation of boiling centers—vapor centers of nucleation which can grow up to critical dimensions.
Let us consider the relationship of the conditions necessary for stable nucleation in dispersephase drops with hydrodynamic parameters of a homoge neous turbulent flow of an emulsion [4]. Let us limit ourselves to the following simplifying model ideas. First, it is assumed that the dispersephase drops of an emulsion are metastable, but their temperature is insufficient for stable spontaneous nucleation having a fluctuation nature [5]. Second, drops with typical size dmin exceeding the turbulence microscale λ0 capable of boiling up are considered. The collisions of vortices with superheated drops are accompanied by the exchange of energy of turbulent motion of the contin uous medium of the emulsion. The phenomenon of resonance at which the effi ciency of transfer of turbulence energy is the highest and the drop can be destroyed under the effect of tur bulent pulsations was studied in [6, 7] on the basis of analysis of the standing capillary waves on the surface of the liquid sphere. For smaller drops, when the char acteristic frequency of turbulent pulsations of the con tinuous medium coincides with the frequency of its intrinsic fluctuations, the external turbulence energy alone is not always sufficient for their guaranteed destruction. The heat energy can also be insufficient for the formation of fluctuation centers of nucleation of vapor as a result of only superheating of such drops. The resonance mechanism of the initiated nucle ation is analogous to the mechanism of fine fragmen tation considered in [8] in the presence of preliminar ily accumulated defects in liquids. In this case, the appearance of defects is due to partial local weakening of the continuity of drops under resonance enhance ment of the turbulent pulsation of pressure in them. In the thermodynamic sense, the stretched state of liq uids due to negative pulsations of pressure is a factor identical to superheating from the standpoint of the theory of homogeneous nucleation [9].
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The intrinsic fluctuations of a drop of an ideal liq uid are characterized by the frequencies fn [6]:
(2πf n) 2 =
8 ( n − 1) n ( n + 1)( n + 2) σ1 , [(n + 1) ρd + nρc] d 3
where n = 2, 3, …; ρd, ρс are the density of the disperse phase and continuous medium, respectively; and σ1 is the coefficient of interphase tension. The frequencies starting from the most energy consuming at n = 2 correspond to oscillatory motion of the sphere:
f 2 res = 2.2
σ1 . [3ρd + 2ρc ] d 3
(1)
Wturb > W0, holds, where W0 is the total excess energy of formation of a critical bubble, and Wturb is the energy of turbulent pulsations. According to the existing thermodynamic ideas [5], the value W0 is determined as
16πσ32 2 2 3 ( ps − p*) (1 − ϑ*/ϑ**)
(2) ⎡ d σ2 ⎤ 2 L T , × ⎢1 + −3 σ2 dT ⎥⎦ ⎣ ( ps − p*)( ϑ** − ϑ*) where ps is the pressure of the saturated vapors (in the first approximation, it is determined by the Antoine equation [10]); p* is the pressure of the liquid phase; ϑ * and ϑ** are the specific volumes of the liquid and vapor phases, respectively (calculated by an approxi mating cubic polynomial); L is the specific heat of vaporization (it is found by the Watson relation [10]); σ2 is the coefficient of the liquid–vapor surface ten sion (it is determined by a linear approximation); and T is the thermodynamic temperature. The minimum size of drops dmin whose boiling up can be initiated by the energy of the turbulent flow is related to the most energyconsuming vortices of comparable value 2
3 Kresρc v d min ≥ W0 ,
2
ment of the pressure pulsations, v is the average value of the square of the difference of the pulsating velocities at the distance of the drop size dmin, and ρ c is the density of the continuous medium. As an example, the further consideration is limited to a homogeneous turbulent flow in a pipeline at a quite high Reynolds number exceeding 10 000. The value of the average square of the difference of the pul sating velocities is determined only by the energy con sumption per unit of mass in unit of time ε
v
The energy of the turbulent vortex upon collision is spent on the deformation of the surface and the increase in the kinetic energy of the oscillatory motion of the liquid inside the drop. It is assumed that initi ated boiling is possible when the energy Wturb obtained and enhanced by the drop owing to resonance interac tion exceeds the total excess energy W0 sufficient for the formation of a critical bubble. Thus, turbulent pul sations can initiate boiling up of superheated drops when the inequality
W0 =
where Kres is the coefficient of resonance enhance
2
2
≈ ( εdmin ) 3 , ε =
λ u03 , 2D
where λ = 0.3164 is the coefficient of hydraulic resis Re 0.25 tance (Re is the Reynolds number), and u0 is the velocity of motion of the emulsion in a pipeline with diameter D averaged over consumption. Taking into account these relations and after addi tional transformations, the minimum size of drops capable of boiling up in collisions with turbulent vorti ces is written as follows: (3) d min = CW00.27µ c−0.05 , where С is an experimental constant, and μс is the dynamic viscosity of the continuous medium deter mined by the Andrade relationship [10]. ANALYSIS OF THE OBTAINED RELATIONS Let us estimate the maximum velocities arising in the resonance oscillations of drops with the diameter of 1 and 100 μm and amplitude of the oscillations equal to the diameter of the drop of the water–organo silicon liquid PES5 emulsion. In the case of har monic oscillations at n = 2, the speed v max = 2π f 2d in accordance with formula (1) has the values vmax ≈ 50 m/s for the diameter of 1 μm and vmax ≈ 5 m/s for the diameter of 100 μm. Figure 1 shows the results of model calculations of the dependence of the total excess energy W0 of for mation of the critical bubble according to (2) at р* = 105 Pa on the superheating temperature in a drop of the emulsion and the dependence of the kinetic energy of energycontaining vortices of the continuous medium at the velocity of 5 and 50 m/s on the drop diameter. At the temperature superheating ΔТ = 10 K, the value of the total excess energy of formation of the critical bub ble W0 = 7 × 10–12 J. At Kres = 1, the minimum kinetic energy of turbulent pulsations Ek transferred to drops with the size d = 1 μm is 1.3 × 10–12 J, and with the size d = 100 μm is 1.3 × 10–8 J. Thus, in the first case, the energy of turbulent flow is not sufficient for initiation of boiling up of micron drops, and in the second case, the probability of initi HIGH TEMPERATURE
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HYDRODYNAMIC ASPECTS OF BOILING UP OF A DISPERSE PHASE
40
dmin, μm 80 120
160
dmin, μm 100
200
−5
3
−5
−7
2
−7
−9
−9
−11
−11
−13
−13 1
−15 −17 0
40
80
120 ΔT, K
−15 160
1
80 logEk
logW0
0
145
−17 200
Fig. 1. Dependences of the total excess energy of the for mation of the critical bubble W0 in J on the superheating value ΔT , K (1) and kinetic energy of the pulsations of the turbulent vortex Ec in J on the drop diameter dminof the water–organosilicon liquid PES5 emulsion: (2) v = 5 m/s; (3) v = 50 m/s.
2
60
40 3 20 0 −50
0
50
100
150
200 ΔT, K
Fig. 2. Dependence of the minimum diameter dmin on the temperature superheating ΔT under the resonance mech anism of initiated boiling up of the water–organosilicon liquid PES5 emulsion: (1) р* = 105 Pa; (2) р* = 0; (3) р* = –105 Pa.
ated boiling up is quite high. This conclusion is con firmed by the results of the experimental study per formed in [1, 2, 11], where the time delays of boiling up of the emulsion were observed; moreover, they increase with the decrease in the diameter of the drops. Figure 2 shows the estimates of the minimum diameter dmin of the dispersephase drops of the water–organosilicon liquid PES5 emulsion under the resonance mechanism of initiated boiling up obtained from relation (3). The calculation curves represent the boundary of the area of the time delay of initiated boil ing up in monodisperse emulsions for pressures of 105, 0, and –105 Pa. Qualitatively, these curves agree well with the experimental results [1, 2, 11]. In the presence of the disperse phase of the zones of local vacuum (curve 2) in the volume and “negative pressure” (curve 3), drops in a definite size range can boil up without a time delay. This is confirmed by the results of the experimental study for the water–organosilicon liquid PES300 emulsion [12].
pulsations on the superheating temperature was obtained. This allows taking into account the effect of hydrodynamic factors on the time delay of boiling up of emulsions with the lowboiling disperse phase and broadening our understanding of the possible mecha nisms of the bubble mode of boiling with the highest intensity of heat transfer.
CONCLUSIONS
4. Rozentsvaig, A.K. and Strashinskii, Ch.S., Initiated Boiling of a Liquid Emulsion with the LowBoiling Dispersed Phase in a Homogeneous Turbulent Flow, in Proektirovanie i issledovanie tekhnicheskikh sistem. Mezhvuzovskii sbornik nauchnykh trudov. Vypusk 11 (An Interdisciplinary Collected Volume of Scientific Works on Design and Investigation of Technical Sys tems), Naberezhnye Chelny (Russia): INEKA, 2008, issue 11, p. 160 [in Russian].
Results of the analysis of the conditions of stable nucleation in the lowboiling disperse phase taking into account the turbulent mode of motion of liquid emulsions were presented. The calculated relation (3) for estimating the dependence of the minimum size of drops whose boiling up can be initiated by the reso nance mechanism of their destruction by turbulent HIGH TEMPERATURE
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REFERENCES 1. Bulanov, N.V. and Gasanov, B.M., Characteristic Fea tures of the Boiling of Emulsions Having a LowBoiling Dispersed Phase, Inzh.–Fiz. Zh., 2006, vol. 79, no. 6, p. 81 [J. Eng. Phys. Thermophys. (Engl. transl.), 2006, vol. 79, no. 6, p. 1130]. 2. Gasanov, B.M., Bulanov, N.V., and Baidakov, V.G., Boiling Characteristics of Emulsions with a LowBoil ing Dispersed Phase and Surfactants, Inzh.–Fiz. Zh., 1997, vol. 70, no. 2, p. 184 [J. Eng. Phys. Thermophys. (Engl. transl.), 1997, vol. 70, no. 2, p. 179]. 3. Rozentsvaig, A.K., EnergySaving Structures of Trans fer Processes in Complex Dispersed Systems, Doctoral Dissertation in Techniques, Kazan: Kazan Power Engi neering University, 2004.
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5. Skripov, V.P., Metastabil’naya zhidkost’, Moscow: Nauka, 1972. Translated under the title Metastable Liq uids, New York: Wiley, 1974. 6. Karabelas, S.A.J., Drop Size Spectra Generated in Tur bulent Pipe Flow of Dilute Liquid–Liquid Dispersions, Am. Inst. Chem. Eng. J., 1978, vol. 24, no. 2, p. 170. 7. Sevik, M. and Park, S.H., The Splitting of Drops and Bubbles by Turbulent Fluid Flow, J. Basic Eng., 1973, no. 1, p. 122. 8. Zeigarnik, Yu.A., Ivochkin, Yu.P., Grigor’ev, V.S., and Oksman, A.A., Notes Concerning Some Aspects of Vapor Explosion, Teplofiz. Vys. Temp., 2008, vol. 46, no. 5, p. 797 [High Temp. (Engl. transl.), 2008, vol. 46, no. 5, p. 734]. 9. Vinogradov, V.E. and Pavlov, P.A., The Boundary of Limiting Superheats of nHeptane, Ethanol, Benzene, and Toluene in the Region of Negative Pressures,
Teplofiz. Vys. Temp., 2000, vol. 38, no. 3, p. 402 [High Temp. (Engl. transl.), 2000, vol. 38, no. 3, p. 379]. 10. Reid, R.C., Prausnitz, J.M., and Sherwood, T.K., The Properties of Gases and Liquids, New York: McGraw Hill, 1977. Translated under the title Svoistva gazov i zhidkostei, Leningrad: Khimiya, 1982. 11. Bulanov, N.V., Gasanov, B.M., and Turchaninova, E.A., Results of Experimental Investigation of Heat Transfer with Emulsions with LowBoiling Dispersed Phase, Teplofiz. Vys. Temp., 2006, vol. 44, no. 2, p. 268 [High Temp. (Engl. transl.), 2006, vol. 44, no. 2, p. 267]. 12. Bulanov, N.V., Skripov, V.P., and Khmyl’nin, V.A., Heat Transfer to Emulsion with Superheating of Its Dispersed Phase, Inzh.–Fiz. Zh., 1984, vol. 46, no. 1, p. 5 [J. Eng. Phys. (New York) (Engl. transl.), 1984, vol. 46, no. 1, p. 1].
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