E. Elias

Two-phase critical flow

Abstract Understanding the heat and mass transfer phenomena occurring during critical flow of two-phase mixtures is of primary importance in the safety analyses of pressurized water, boiling water and liquid-metal-cooled nuclear reactors. It has been shown that during a blowdown incident, the critical flow rate of the two-phase mixture may be affected by a variety of parameters such as the fluid stagnation conditions, the configuration of the blowdown vessel, the length and diameter of the exhaust duct, the purity of the liquid and the local and frictional pressure losses in the flow channel. The complexity of the thermodynamic phenomena taking place during the blowdown process resulted in many studies which compare a particular theory with selected sets of experimental data. However, in the absence of an adequate theory which is applicable over the entire range of the parameters encountered in the nuclear industry, there is a tendency to rely on semi-empirical correlation of the existing data. The main objective of this paper is to provide a general review of two-phase critical flow from the viewpoint of the needs of thermal-hydraulic systems codes and to conduct a systematic evaluation of the existing data and theoretical models in order to quantify the validity, under various conditions, of several of the more widely used critical flow models. Ten different critical flow models have been formulated and tested in this study against an extensive set of data from critical flow experiments with water as the test fluid. Results of the present study are expected to enhance the understanding of the predictive capabilities and limitations of the critical flow models currently used in the power industry.

Unsteady conjugated heat transfer in laminar pipe flow

Abstract This study analyses the transient conjugated heat transfer in laminar pipe flow, where the flow is both hydrodynamically and thermally fully developed. Two cases are considered: a prescribed constant wall temperature and a constant heat flux at the wall. A non-standard method of separation of variables is applied, which treats the fluid and the solid as one region with certain discontinuities. The resulting eigenfunctions, which are not orthogonal to each other with respect to the usual weight function according to the Sturm-Liouville theorem, are made orthogonal to each other with respect to a special weight function. It is concluded that the degree of conjugation and viscous dissipation may have a great impact on the temperature distribution in the fluid.

Flow and Heat Transfer Regimes During Quenching of Hot Surfaces

Abstract An experimental and theoretical study of flow and heat transfer regimes during quenching of a heated vertical channel is presented. The objective of the experimental portion of the research was to obtain quantitative data and observations on the reflooding of an annular channel typical to small research reactors. Data were used to assist the formulation of a theoretical model to predict the rate of precursory cooling during reflooding. Tests were carried out at constant inlet pressure using subcooled water as a working fluid. Measurements included inlet and outlet flow conditions, vapor and liquid temperatures along the test section and the volumetric void fraction as a function of distance from the quench front. Surface heat flux was calculated from the fast temperature measurements along the heated surface. The quench front is shown to lie in the transition boiling region which spreads into the dry and wet segments of the surface.

Bubble transport in flashing flow

Abstract A bubble transport equation, based on the theory of bubble nucleation and growth, is applied for the analysis of two-phase flashing flows. Spontaneous nucleation at the flashing inception point and heterogeneous nucleation in the liquid bulk are used as boundary and initial conditions, respectively. Analytical solution of the transport equation yields a constitutive relation for the net vapor generation rate along the tube, which is required for closure of a two-fluid set of conservation and balance equations. Model predictions, in terms of flow rates and void fraction distributions, compare favorably with measured data. A mechanistic representation of the thermodynamic and transport conditions at the flashing inception point is described.

The relation between the rewetting temperature and the liquid-solid contact angle

FIG. 6. The locus of the position of the triple points for d,, = 2, and for L = 0.2,0.1,0.05, and 0.01. plane between these two curves in which the most unstable modes are oscillatory. The width of this region appears to diminish with decreasing (I and thus may not be discernible in these figures for lower values of cr, but nevertheless it exists. The position of the solid curves in both Figs. 4 and 5 represents an absolute lower bound for the instability region in the first quadrant of the R-Rs plane. This is to say that any basic state contiguration for which both R and Rf fall above that curve is linearly unstable. Thus the location of this curve is valuable as a general stability criteria for double diffusive conv~tion. Figure 6 shows the various envelope curves formed by the loci of the tripie points for four Lewis numbers. Two significant features may be observed in this figure. The first is that all curves shown originate from a single point on the ordinate. This is the location of the critical point for AS = 0. The second is that the inclination of each curve to the abscissa appears to increase with decreasing values of L. It may be concluded on the basis of this figure that the region in which the monotone unstable modes are dominant diminishes with decreasing L for any one value of fi. However, this does not imply an equivalent increase in the stability region since, as was shown earlier, the size of that region is a function of 6. Depending on the value of a there could be a substantia1 inl..?. Heut Mass

VOID FRACTION DISTRIBUTION IN LOW FLOW RATE SUBCOOLED BOILING

Experimental data are presented for the void fraction distribution in low flow rate forced convection subcooled boiling of water in a heated vertical tube at steady-state conditions. The measurements are based on gamma attenuation and X-ray radiography techniques. The measured local equilibrium quality at the point of net vapor generation and the void fraction profiles are compared with theoretical and empirical models of subcooled boiling. A close fit to the experimental results is obtained by the Levy model and by the Saha and Zuber correlation.

Low energy photons from 152gEu for Ge(Li) calibration

Abstract Intensities of low energy gamma and X-rays in the decay of 12.4 y 152 Eu were measured. A branching ratio of 1.84±0.17 between the decay by β − emission to 152 Sm and via EC and β + to 125 Gd, was found from the relative X-rays and 344 keV intensities. The measured energies in keV and the absolute intensities in photons per 100 disintegrations are: 39.5±0.2(45. 3 ±5.8), 45.2±0.2 (11. 2 ±1.4), 121.9±0.1 (27. 7 ±3.1), 244.75±0.08(7.5 2 ±0.85), 295.8±0.1 (4.5 3 ±0.61), 344.44±0.09 (24. 5 ±2.7), 367.8±0.2 (0.72 1 ±0.086), 411.3±0.2 (1.9 4 ±0.24), 444.2±0.2 (2.9 6 ±0.33) The nucleus is recommended as a calibration standard for Ge(Li) detectors.

A two-fluid model for critical flashing flows in pipes

Abstract A one-dimensional two-fluid model is described for the analysis of critical flows in pipes of nondiverging cross-sectional area. The model accounts for thermal nonequilibrium between the liquid and vapor bubbles and for interphase relative motion. Closure of the set of governing equations is performed with constitutive relationships which determine the pressure drop along the flow channel as a function of the flow regime, and the number and rate of growth of vapor bubbles in a variable temperature field in terms of the problems primary state variables and geometrical configuration. An empirical correlation is derived which fits the number density of bubble nuclei in the flow as a function of the flow channel length-to-diameter ratio. Model predictions compare favorably with experimental data in small- and large-scale systems over a wide range of pressures and pipe diameters and lengths.

Inverted-annular film boiling heat transfer from vertical surfaces

Abstract A theoretical model is developed which allows a consistent treatment of the wall heat flux in an inverted-annular film boiling regime. The model is based on an analytical solution of the energy conservation equations in the vapor and liquid regions downstream of the quench front. A constant vapor film thickness is assumed, which depends on the fluid equilibrium quality at the quench front. Good agreement is obtained in comparing the model with quasi-steady state experimental results.

Artificial neural networks optimization method for radioactive source localization

An optimization artificial neural networks model is developed for solving the ill-posed inverse transport problem associated with localizing radioactive sources in a medium with known properties and dimensions. The model is based on the recurrent (or feedback) Hopfield network with fixed weights. The source distribution is determined based on the response of a limited number of external detectors of known spatial deployment in conjunction with a radiation transport model. The algorithm is tested and evaluated for a large number of simulated two-dimensional cases. Computations are carried out at different noise levels to account for statistical errors encountered in engineering applications. The sensitivity to noise is found to depend on the number of detectors and on their spatial deployment. A pretest empirical procedure is, therefore, suggested for determining an effective arrangement of detectors for a given problem.