Superheated-liquid model

The second RPT criterion relates to the temperature of the hot liquid. That is, this temperature must exceed a threshold value before an RPT is possible. From one theory of RPTs, the superheated-liquid model (described later), this criterion arises naturally, and the threshold hot-liquid temperature is then equal to the homogeneous nucleation temperature of the colder liquid T. This temperature is a characteristic value for any pure liquid or liquid mixture and can be measured in independent experiments or estimated from theory. From alternate RPT theories, the threshold temperature may be equated, approximately, to the hot fluid temperature at the onset of stable film boiling. 

The superheated-liquid model introduced earlier to explain LNG-water RPTs was not considered applicable for smelt-water explosions since the very large temperature difference between the smelt and water would, it... 

Thus, it would appear that overpressures experienced in the air from LNG RPTs for spills less than about 30 are not particularly large unless one is very close to the spill site. Overpressures in the water are much larger, as shown in Table X from transducer measurements about 0.7 m from the surface. In fact, in one instance, the overpressure in the water exceeded the critical pressure of the LNG this would not have been expected from the superheated liquid model. 

In this article, we suggest that a modified superheated-liquid model could explain many facts, but the basic premise of the model has never been established in clearly delineated experiments. The simple superheated-liquid model, developed for LNG and water explosions (see Section III), assumes the cold liquid is prevented from boiling on the hot liquid surface and may heat to its limit-of-superheat temperature. At this temperature, homogeneous nucleation results with significant local vaporization in a few microseconds. Such a mechanism has been rejected for molten metal-water interactions since the temperatures of most molten metals studied are above the critical point of water. In such cases, it would be expected that a steam film would encapsulate the water to... 

To prove or disprove such a modified superheated-liquid model, experiments are necessary to delineate the rates and products of reaction between molten metals and water in a high-temperature environment with and without substrates which could participate in the reaction. 

Another theoretical basis of the superheated liquid-film concept lies on the irreversible thermodynamics developed by Prigogine [43]. According to this theory, irreversible chemical processes would be described (Equation 13.17) by extending the equation of De Donder, provided that simultaneous reactions were coupled in a certain thermodynamic model, as follows ... 

Fig. 16. Calculated phase diagram of the soft-sphere plus mean-field model, showing the vapor-liquid (VLB), solid-liquid (SI.E ), and solid-vapor (SVE) coexistence loci, the superheated liquid spinodal (s), and the Kauzmann locus (K) in the pressure-temperature plane (P = Pa /e-,T =k T/ ). The Kauzmann locus gives the pressure-dependent temperature at which the entropies of the supercooled lit]uid and the stable crystal are equal. Note the convergence of the Kauzmann and spinodal loci at T = 0. See Debenedetti et al. (1999) for details of this calculation.

The above observation has a physical interpretation. The unavailable region BD of the isotherm, at a continuous evolution on the catastrophe surface, corresponds to the region bounded by the curve BKC in Fig. 38. The sections AB and CD correspond to the superheated liquid and the supercooled vapour, respectively. It should be emphasized that the unavailability of the states BD derives from a model of the A3 catastrophe provided... 

A theoretical model for the heterogeneous nucleation was proposed by Hsu [10] for the growth of pre-existing nuclei in a cavity on a heated surface. The model included the effect of nmi-uniform superheated liquid. The equation for the activation curve of bubble nucleation was derived by combining the Clausius-Qapeyron and the Young—Laplace equations. Then, by substituting the linear temperature profile into the equation, the range of active cavity sizes on the heated surface was obtained. 

The theory of bubble nucleation in a superheated liquid was first applied to the concept of thermal inkjet by Allen et al. [7]. They were able to determine the minimum cmiditions for the first bubble nucleation by applying Hsu s theory [10]. Time dependent temperature profiles above a heater surface were obtained. By superimposing the activation curve with the thermal boimdary layer, the initial bubble size and the minimum temperature for nucleation were determined. Based on a one-dimensional model and by assuming the nucleation temperature to be the superheat limit of the liquid at 330°C transient temperature profiles for the heater structure and the bubble surface after nucleation were obtained. It was noticed that the decay time to ambient temperature from its initial state was only several microseconds after 6 ps heating pulse. The thermal effects of the passivation (protective coating) layer on the heater surface were also analyzed. The results showed that the effective pulse energy required for bubble nucleation increases with the thickness of the passivation layer. 

Experiments with rapid decompression of superheated liquids and droplets exploding near the superheat hmit reveal the existence of steady evaporation waves. An idealized model for steady evaporation waves has been analyzed. A evaporation wave is treated as a jump or discontinuity between metastable liquid and an equilibrium vapor or liquid-vapor mixture. 

This wave model is combined with a simple similarity description of liquid and vapor motion to predict the rates of steady spherical bubble growth in superheated liquids. The Chapman-Jouguet hypothesis is used to fix the evaporation rate and the results are compared with observations in bubble column experiments. 

Subsonic evaporation waves can be combined with a simple similarity solution to the radial continuity and momentum equations to obtain [13] an idealized model for rapid bubble growth in superheated liquids. This model is based on the experimental observations [1,2,5] that the bubble radial velocity and evaporative mass fiux are approximately constant for the explosive boiling mode of evaporation near the superheat limit. 

Johnson, D. W. 1991. Prediction of Aerosol Formation from the Release of Pressurized, Superheated Liquids to the Atmosphere, in Proceedings of International Conference and Workshop on Modeling and Mitigating the Consequences of Accidental Releases of Hazardous Materials, New Orleans, May 20-24, American Institute of Chemical Engineers, New York, pp. 1-34. 

Equilibritun flash models for superheated liquids are based on thermodynamic theory. However, estimates of the aerosol fraction entrained in the resultant cloud are mostly empirical or semiempirical. Most evaporation models are based on the solution of time dependent heat and mass balances. Momentum transfer is typically ignored. Pool spreading models are based primarily on the opposing forces of gravity and flow resistance and typically assume a smooth, horizontal surface. 

The output of flash models is the vapor-liquid split fi-om a discharge of a superheated liquid. Aerosol and rainout models provide estimates of the fractions of the liquid that remain suspended within the cloud. 

Muralidhar, R., G. R. Jersey, F. J. Krambeck, and S. Sundaresan (1995). A Two-Phase Model for Subcooled and Superheated Liquid Jets. International Conference and Workshop on Modeling and Mitigating the Consequences cf Accidental Releases [Pg.345]

All modules use the 2-fluid model to describe steam-water flows and four non-condensable gases may be transported. The thermal and mechanical non-equilibrium are described. All kinds of two-phase flow patterns are modelled co-current and counter-current flows are modelled with prediction of the counter-current flow limitation. Heat transfer with wall structures and with fuel rods are calculated taking into account all heat transfer processes ( natural and forced convection with liquid, with gas, sub-cooled and saturated nucleate boiling, critical heat flux, film boiling, film condensation). The interfacial heat and mass transfers describe not only the vaporization due to superheated steam and the direct condensation due to sub-cooled liquid, but also the steam condensation or liquid flashing due to meta-stable subcooled steam or superheated liquid. 

Ge and Fan (2005) developed a 3-D numerical model based on the level-set method and finite-volume technique to simulate the saturated droplet impact on a superheated flat surface. A 2-D vapor-flow model was coupled with the heat-transfer model to account for the vapor-flow dynamics caused by the Leidenfrost evaporation. The droplet is assumed to be spherical before the collision and the liquid is assumed to be incompressible. 

For small-scale experiments, the LNG and liquid refrigerant cases are analyzed using a model which assumes that the volatile liquid (or some part of it) is superheated to a temperature at which homogeneous nuclea-tion occurs. Such nucleation is very rapid and the event resembles an explosion. An attempt is made to employ this same model to explain R s in the water-smelt, water-aluminum, and water-reactive metal cases, but data to make definitive conclusions are lacking. 

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