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Gradient theory for the description of interfacial phenomena in flashing water flows

Banaszkiewicz M., Badur J.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2000

Vol. 4, No 2

213-290

The present work concerns the description of phenomena taking place within interfacial regions during a flow of water, which is accompanied by heterogeneous flashing. The main aim of the work is to present a unified approach to first order phase transitions with the inclusion of capillary effects and to built on this basis a mathematical model describing nonequilibrium two-phase flows, in which the properties of the mixture include capillary components. The analysis of the problem was started with a discussion of physical aspects of flashing, which are the contents of Chapter 2. On the basis of the experimental data analysis a physical model of the phenomenon was formulated. In Chapter 3 a gradient description of first order heterogeneous phase transitions was given. The analysis was begun with a discussion of the properties and structure of interfacial areas. On the basis of the analysis constitutive equations for reversible stress tensor and free energy of a two-phase system treated as a homogeneous medium were formulated. The constitutive equations include capillary components modelled by means of the dryness fraction gradients and resulting from the nonuniformity of the system caused by the existence of two phases and interfacial surfaces. On the basis of the proposed theory a homogeneous model of two-phase flow with capillary effects was derived, which is a subject of Chapter 4. Taking into consideration the assumptions of the homogeneous model, one-dimensional balance equations for mass, momentum and energy of the mixture and mass of vapour were derived. A constitutive equation for the source term appearing in the last equation was obtained on the basis of the theory of internal parameters with the usage of the proposed form of free energy including a gradient term known from the second gradient theory. The remaining constitutive equations for the density of the two-phase system, wall shearing stresses and capillary pressure were also given. The proposed mathematical model was investigated from the point of view of wave properties, which were discussed in Chapter 5. The analysis of small disturbations was conducted, as a result of which a dispersion equation was obtained giving a relation between the velocity of disturbations, attenuation coefficient and frequency. This dispersive model was then applied for the prediction of critical mass flux in a channel flow using PIF method. On the basis of the comparison of the model predictions with experimental measurements a reasonably good agreement was found. In Chapter 6 the results of numerical calculations of flashing flow in channel were presented. Since the proposed mathematical model contains several phenomenological coefficients, a parametric analysis was performed in order to determine their value and the influence on solutions. For the sake of the analysis the classical benchmark experiment known as the Moby Dick was used. After fitting the solution of the model into the experimental measurements new calculations for other runs and other experiments were carried out. As a result of the analysis a good agreement of the model with reality was found, as well as its usefulness for the calculations of pressure and void fraction distributions in channels and for the determination of mass flow rate of two-phase systems. It constitutes a confirmation of the correctness of the proposed model as well as the theory on the basis of which it was built.

Predictions of critical mass velocities in flashing water flow by means of second gradient model

Badur J., Banaszkiewicz M. J.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Mechanika

1999

Z. 67

163--172

The paper deals with numerical predictions of critical mass fluxes in two-phase water-steam flows. Special emphasis is laid on the predictions of critical flow rates for nonequilibrium water-steam mixtures. A new mathematical model has been proposed which takes into account the influence of interfaces on mass, momentum and energy transfer. It is a quasi-one-dimensional model for adiabatic channel flows. In order to determine critical mass flux the so-called natural choking criterion has been employed (PIF - possible-impossible flow). Such obtained numerical results have been compared with the results of two benchmark experiments on two-phase critical flows - Moby Dick and BNL. A reasonably good agreement between the predictions of the theoretical model and the experiments has been found.