Two-Phase Vessel Blowdown of an Initially Saturated Liquid—Part 2: Analytical

1983 ◽  
Vol 105 (4) ◽  
pp. 694-699 ◽  
Author(s):  
M. N. Hutcherson ◽  
R. E. Henry ◽  
D. E. Wollersheim
Keyword(s):  
Bubble Growth ◽  
Growth Analysis ◽  
Initial Period ◽  
Saturation Pressure ◽  
Equilibrium Analysis ◽  
Analytical Models ◽  
Superheated Liquid ◽  
Saturated Liquid ◽  
Two Phase ◽  
System Pressure

Analytical models are presented to predict the internal vessel conditions during the decompression regimes of an initially saturated liquid. A subcooled blowdown analysis considers the elasticity of both the liquid and vessel. A bubble growth analysis for the intermediate period of blowdown is based on thermally dominated bubble growth from a solid surface into a superheated liquid. A dispersed analysis for the latter decompression period assumes the vapor bubbles have grown sufficiently so the liquid is uniformly distributed within the vapor phase. The sub-cooled analysis predicts the initial period of blowdown reasonably well. The bubble growth analysis predicts the rise in system pressure above that value to which it initially falls after the end of subcooled blowdown. It considers an initially “slow” depressurization rate (less than 400 MPa/s) where nucleation and bubble growth is the dominate volume producing, and thus pressure recovery, mechanism. It provides insight into why the system pressure initially drops below the saturation pressure, and it also offers an explanation for the subsequent recovery of the system pressure toward the saturation pressure. The thermodynamic equilibrium analysis provides a reasonable prediction of the latter stage of decompression. The combination of these three models predicts the overall two-phase decompression phenomenon reasonably well.

On the Equilibrium of Cavitation Nuclei in Liquid-Gas Solutions

1981 ◽  
Vol 103 (3) ◽  
pp. 425-430 ◽  
Author(s):  
Y. S. Cha
Keyword(s):  
Stable Equilibrium ◽  
Thermodynamic Theory ◽  
Phase System ◽  
Saturated Liquid ◽  
Theoretical Justification ◽  
Two Phase ◽  
System Pressure ◽  
Two Component ◽  
Cavitation Nuclei ◽  
The Stability

The stability of a spherical bubble in a two-component two-phase system is examined by employing the thermodynamic theory of dilute solutions. It is shown that a bubble can remain in a state of stable equilibrium provided that the ratio of the total number of moles of the solute to the total number of moles of the solvent in the system is not extremely small and that the system pressure falls between an upper bound (dissolution limit) and a lower bound (cavitation limit). The results of the analysis provide a theoretical basis for the persistence of microbubbles in a saturated liquid-gas solution. Thus to a certain extent, the results also help to resolve the dilemma that exists in the field of cavitation due to (1) the necessity of postulating the existence of microbubbles; and (2) the lack of theoretical justification for the persistence of such bubbles in a liquid.

Two-Phase Vessel Blowdown of an Initially Saturated Liquid—Part 1: Experimental

1983 ◽  
Vol 105 (4) ◽  
pp. 687-693 ◽  
Author(s):  
M. N. Hutcherson ◽  
R. E. Henry ◽  
D. E. Wollersheim
Keyword(s):  
Pressure Vessel ◽  
Large Diameter ◽  
Small Diameter ◽  
Nonuniform Distribution ◽  
Superheated Liquid ◽  
Critical Flow ◽  
Saturated Liquid ◽  
Two Phase ◽  
Saturated Water ◽  
Liquid Part

Experimental blowdown results for initially isothermal, saturated water from a small pressure vessel containing internal geometry are presented. This experiment simulated a break in a large duct of approximately three diameters in length which exited from the vessel. Choking only occurred at the exit of the discharge duct, and the instantaneous internal vessel pressure distribution was nearly uniform. Most of the fluid within the vessel immediately after the initiation of the blowdown became superheated liquid. This thermodynamic state together with the activated wall cavities inside the vessel maintained a nearly constant internal vessel pressure history early in the blowdown. However, in the latter stage of the depressurization, the remaining fluid within the vessel was essentially in thermodynamic equilibrium. A nonuniform distribution of fluid quality within the vessel was also detected in this experiment. In addition, this experiment illustrates that transient, two-phase, critical flow in large diameter ducts is similar to steady, two-phase, critical flow in small diameter ducts.

scholarly journals Effect of Heat Transfer on the Growing Bubble with the Nanoparticles/Water Nanofluids in Turbulent Flow

2021 ◽  
Vol 8 (1) ◽  
pp. 95-102
Author(s):  
Ahmed K. Abu-Nab ◽  
Ali F. Abu-Bakr
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Turbulent Flow ◽  
Bubble Growth ◽  
Bubble Dynamics ◽  
Pure Water ◽  
Theoretical Data ◽  
Superheated Liquid ◽  
Two Phase ◽  
The Mathematical Model

This paper is devoted to study the effect of heat transfer on the temperature distribution in a superheated liquid during the growth of vapour bubbles immersed in different types of nanoparticles/water nanofluids between two-phase turbulent flow. The mathematical model is formulated and solved analytically depending on Scriven's theory and using the modification of the method of the similarity parameters between two finite boundaries. The characteristics of vapour bubble growth and temperature distribution are obtained by using the thermo-physical properties of nanoparticles nanofluids. The results indicate that the nanoparticle volume concentration reduces the bubble growth process under the effect of heat transfer. The better agreements are achieved, for bubble dynamics in turbulent nanofluid using the appropriate numerical and theoretical data for the values of concentration rate of nanoparticles χ=0,0.2,0.4. The temperature distribution surrounding the regime of bubble growth in pure water is more intensive than in other cases of Al2O3/H2O, Fe3O4/H2O and CuO/H2O nanofluids in turbulent flow. A Comparison of the current solution with previous works is carried out and discussed.

THE MECHANISM OF RAISING AND QUANTIFICATION OF SPECIFIC HEAT FLUX AT BOILING OF NANOFLUIDS IN FREE CONVECTION CONDITIONS

2017 ◽  
pp. 25-34
Author(s):  
V.N. Moraru
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Capacity ◽  
Specific Heat ◽  
Chemical Properties ◽  
Heating Surface ◽  
Physical Models ◽  
Superheated Liquid ◽  
Two Phase ◽  
Boiling Process

The results of our work and a number of foreign studies indicate that the sharp increase in the heat transfer parameters (specific heat flux q and heat transfer coefficient _) at the boiling of nanofluids as compared to the base liquid (water) is due not only and not so much to the increase of the thermal conductivity of the nanofluids, but an intensification of the boiling process caused by a change in the state of the heating surface, its topological and chemical properties (porosity, roughness, wettability). The latter leads to a change in the internal characteristics of the boiling process and the average temperature of the superheated liquid layer. This circumstance makes it possible, on the basis of physical models of the liquids boiling and taking into account the parameters of the surface state (temperature, pressure) and properties of the coolant (the density and heat capacity of the liquid, the specific heat of vaporization and the heat capacity of the vapor), and also the internal characteristics of the boiling of liquids, to calculate the value of specific heat flux q. In this paper, the difference in the mechanisms of heat transfer during the boiling of single-phase (water) and two-phase nanofluids has been studied and a quantitative estimate of the q values for the boiling of the nanofluid is carried out based on the internal characteristics of the boiling process. The satisfactory agreement of the calculated values with the experimental data is a confirmation that the key factor in the growth of the heat transfer intensity at the boiling of nanofluids is indeed a change in the nature and microrelief of the heating surface. Bibl. 20, Fig. 9, Tab. 2.

Investigation of two-dimensional nonstationary processes of outflow a gas-saturated liquid from axisymmetric vessels

2012 ◽  
Vol 9 (1) ◽  
pp. 47-52
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Buzina
Keyword(s):  
Comparative Analysis ◽  
Numerical Model ◽  
Liquid Mixture ◽  
Phase Model ◽  
Test Problems ◽  
Two Dimensional ◽  
Nonstationary Processes ◽  
Saturated Liquid ◽  
Two Phase ◽  
One Dimensional

The two-dimensional and two-phase model of the gas-liquid mixture is constructed. The validity of numerical model realization is justified by using a comparative analysis of test problems solution with one-dimensional calculations. The regularities of gas-saturated liquid outflow from axisymmetric vessels for different geometries are established.

Effect of Pressure on Bubble Growth Within Liquid Droplets at the Superheat Limit

1982 ◽  
Vol 104 (4) ◽  
pp. 750-757 ◽  
Author(s):  
C. T. Avedisian
Keyword(s):  
Vapor Bubble ◽  
Bubble Growth ◽  
High Speed ◽  
Ambient Pressure ◽  
Organic Liquid ◽  
Liquid Droplets ◽  
Growth Data ◽  
Two Phase ◽  
Photographic Evidence ◽  
Good Agreement

A study of high-pressure bubble growth within liquid droplets heated to their limits of superheat is reported. Droplets of an organic liquid (n-octane) were heated in an immiscible nonvolatile field liquid (glycerine) until they began to boil. High-speed cine photography was used for recording the qualitative aspects of boiling intensity and for obtaining some basic bubble growth data which have not been previously reported. The intensity of droplet boiling was found to be strongly dependent on ambient pressure. At atmospheric pressure the droplets boiled in a comparatively violent manner. At higher pressures photographic evidence revealed a two-phase droplet configuration consisting of an expanding vapor bubble beneath which was suspended a pool of the vaporizing liquid. A qualitative theory for growth of the two-phase droplet was based on assuming that heat for vaporizing the volatile liquid was transferred across a thin thermal boundary layer surrounding the vapor bubble. Measured droplet radii were found to be in relatively good agreement with predicted radii.

Heat Transfer in Porous Media Heated From Above With Evaporation, Condensation, and Capillary Effects

1983 ◽  
Vol 105 (3) ◽  
pp. 485-492 ◽  
Author(s):  
K. S. Udell
Keyword(s):  
Stable State ◽  
Superheated Liquid ◽  
Phase Zone ◽  
Two Phase ◽  
Water Steam ◽  
Zone Length ◽  
Compressed Liquid ◽  
Pressure Lowering ◽  
Darcy’S Equations ◽  
Convection Dominated

Heat and mass transfer characteristics of a sand-water-steam system heated at the top and cooled at the bottom were studied. It was found that at steady-state conditions the system segregated into three regions. The top region was conduction-dominated with the voids containing a stationary superheated steam. The middle region was convection-dominated, nearly isothermal, and exhibited an upward flow of the liquid by capillary forces and a downward flow of steam due to a slight pressure gradient. The bottom portion contained a stationary compressed liquid and was also conduction dominated. The length of the two-phase convection zone was evaluated through the application of Darcy’s equations for two-phase flow and correlations of relative permeabilities and capillary pressure data. The model was in excellent agreement with the observed results, predicting a decreasing two-phase zone length with increasing heat flux. The thermodynamics of the two-phase zone were also analyzed. It was found that the vapor phase was in a superheated state as described by the Kelvin equation for vapor pressure lowering. Also, it was evident that the liquid must also be superheated for thermodynamic equilibrium to result. A stability analysis demonstrated that the superheated liquid can exist in an unconditionally stable state under conditions typical of porous systems. The degree of liquid superheat within the two-phase zone of these experiments was obtained.

Collective Effects on the Growth of Vapor Bubbles in a Superheated Liquid

1984 ◽  
Vol 106 (4) ◽  
pp. 486-490 ◽  
Author(s):  
G. L. Chahine ◽  
H. L. Liu
Keyword(s):  
Collective Behavior ◽  
Bubble Growth ◽  
Theoretical Study ◽  
Pressure Field ◽  
Bubble Radius ◽  
Significant Inhibition ◽  
Collective Effects ◽  
Superheated Liquid ◽  
Vapor Bubbles ◽  
Bubble Interaction

The problem of the growth of a spherical isolated bubble in a superheated liquid has been extensively studied. However, very little work has been done for the case of a cloud of bubbles. The collective behavior of the bubbles departs considerably from that of a single isolated bubble, due to the cumulative modification of the pressure field from all other bubbles. This paper presents a theoretical study on bubble interaction in a superheated liquid during the growth stage. The solution is sought in terms of matched asymptotic expansions in powers of ε, the ratio between rb0, a characteristic bubble radius and l0, the interbubble distance. Numerical results show a significant inhibition of the bubble growth rate due to the presence of interacting bubbles. In addition, the temperature at the bubble wall decreases at a slower rate. Consequently, the overall heat exchange during the bubble growth is reduced.

Analytical models for bubble growth during decompression of high viscosity magmas

1995 ◽  
Vol 57 (6) ◽  
pp. 422-431 ◽  
Author(s):  
J. Barclay ◽  
D. S. Riley ◽  
R. S. J. Sparks
Keyword(s):  
Bubble Growth ◽  
High Viscosity ◽  
Analytical Models
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