Interfacial Friction Factor for High-Pressure Steam/Water Stratified-Wavy Flow in Horizontal Pipe

The interfacial friction was investigated for high-pressure (3 to 9 MPa) steam/water stratified-wavy flow, using the TPTF experimental data for 4 and 8-inch diameter horizontal pipe test sections. The interfacial waves observed in the stratified-wavy flow regime with void fractions typically <–0.6, became larger in r.m.s. amplitude and more irregular in both amplitude and wave length, as the transition boundary to slug flow was approached. A correlation to predict the interfacial friction factor has been obtained for the stratified-wavy flows including the vicinity of the transition boundary to slug flow. The correlation is based on two non-dimensional parameters related to the interfacial wave generation by the Kelvin-Helmholtz instability, and correlates the TPTF data taken under different pipe diameters and pressures.     

Vertically Downward Two-Phase Flow, (I)

Fully developed vertically downward two-phase flow of air-water mixture was investigated on void distribution and average void fraction among the three basic flow regimes; bubbly, slug and annular flows. The annular flow further was divided into two regimes of falling film flow and annular drop flow. Test channel is in form of inverted U-tube and tests were carried out at 100 tube diameters downstream from the curved part. Distributions of local void fraction were measured by means of a conductance needle probe method and the average void fraction was obtained from numerical integration of the measured local void fraction According to the results, profiles of local void fraction in bubby and slug flows showed characteristic natures with a peak in the middle region between the center and the wall of tube The average void fraction in downward flow depended greatly on the flow regimes. Accordingly correlation for each flow regime was developed to predict the average void fraction, based on flow mechanisms and experiments. The correlations were compared with experimental results for atmospheric air-water flow and showed satisfactory agreement.     

Vertically Downward Two-Phase Flow, (II)

Following Part (I) of the present paper, which presented the experimental results obtained on the void distribution and average void fraction shown by nearly fully-developed, vertically downward two-phase flow of air-water mixture, this Part (?) covers the flow regime transition criteria among the three basic flow regimes : bubbly, slug and annular flows. The annular flow further was divided into two subregions of falling film flow and annular drop flow. The general situation of the transition criteria is as follows : (1) bubbly-to-slug flow transition occurs when the local void fraction in the central region of the tube is 0.3; (2) slug-to-annular drop flow transition criterion is given as a case which equations giving average void fraction for the slug flow and the annular flow are simultaneously satisfied; (3) slug-to-falling film flow transition occurs when the pressure difference between the crest of large wave and the bottom overcomes the surface tension; (4) the occurrence of liquid droplets from wave crests gives the transition criterion between the falling film flow and the annular drop flow.

These criteria were correlated to predict each flow regime boundary respectively considering flow mechanisms or from experimental results. The correlations obtained were compared with published flow regime maps for atmospheric air-water flow and showed satisfactory agreement.     

Hydrodynamic and Hydraulic Studies on Void Fractions in Two-Phase Flow

For gas-liquid two-phase flow, two kinds of fundamental equations have been proposed by the methods of hydrodynamics and hydraulics. The hydrodynamic equation, to avoid analytical difficulties, does not deal with two-phase flow itself, but with a hypothetical liquid flow which has actual physical quantities in the region where the liquid phase really exists and has the imaginary physical quantities of liquid in the region where the gas exists, for each instant, and with a hypothetical gas flow similarly. The hydraulic equation differs from the usual form in the treatment of friction term or interaction, and has better physical insight. These equations are analyzed mathematically and some relationship between physical quantities centering void fraction are discussed. Hydrodynamic equation shows the void fraction distribution to have relation to pressure loss and velocity distributions, and, for the case of laminar two-phase flow with axial symmetry, explicit expression is presented. By hydraulic equation, the relation between void fraction and other variables are discussed. For the upward two-phase flow with constant flow area, gas-liquid interaction force is discussed theoretically and experimentally.     

矩形窄缝通道内水沸腾流型理论研究

对矩形窄缝通道(1×20mm,2×20mm)中水沸腾的汽液两相流动流型转化准则进行了研究。根据实验结果,水平矩形窄缝加热通道中流型可以分为泡状流、间歇弹状流、搅拌流、环状流和汽液分离流。运用分相流模型对矩形窄缝通道中水沸腾的汽液两相流动流型进行了理论分析,得出了相应的流型转换准则,并与实验数据进行了初步比较,符合较好。     

Electrical Conductivity of Liquid Metal Two-Phase Mixture in Bubbly and Slug Flow Regime

A correlation function for reactor noise is determined through a conditional polarity-correlation technique in which the polarity of neutron-counting fluctuations is analyzed with the start condition that the counting rate reaches a preset level. This technique, evidently, is an example of flash-start technique, developed for the purpose of improving the efficacy of reactor noise analysis. In the present case, the conditional polarity-correlation function is described mathematically assuming that the counting fluctuations of the detector conform with a Gaussian distribution. The expression thus derived reveals that this function is approximately proportional to a cross-correlation function and is a differential type of polarity-correlation function.

In order to examine the validity of the obtained expression, an experiment was performed in a graphite-moderated reactor at slightly subcriticai state to measure the conditional polarity-correlation function. A novel contrivance was adopted in the experiment to eliminate the dead-time effect created during the busy time of the multi-channel time analyzer. The dependence on the preset level—i.e. flash-start condition—exhibited by the conditional polarity—correlation function showed good agreement with that expected from the mathematical expression. The prompt mode neutron decay constants were determined from the experimental data within statistical error of 3～4 %.     

Safety Relief Valve Performance for Two-Phase Flow

The performance of main steam safety relief valve has been evaluated with respect only to the steam. In the present study, two-phase flow and subcooled water blow-out tests with model valves were performed in order to evaluate the valve's characteristics and performance. From the test results, it was made clear that not only for the steam but also for the two-phase flow the measurement data were hardly affected by scaling and also that the reaction force of the fluid to the valve stem was hardly dependent upon the void fraction. Analytical study was performed using the two-phase flow model in the valve. The results of the analysis showed good agreement with the test data. It was shown from the test and analysis results that the reaction force of the two-phase flow and subcooled water to the valve stem was almost as much as that of the steam flow, and the integrity of the safety relief valve could be maintained.     

Experimental Study of Counter-Current Two-Phase Flow in Horizontal Tube Connected to Inclined Riser

In order to determine the Counter-Current Flow Limitation (CCFL) in hot legs of PWRS, CCFL characteristics of air-water and saturated steam-water flow were experimentally investigated in a modeled flow path of a horizontal tube connected to an inclined riser. The ranges of dimensions of experimental tubes were as follows: diameter D 0.026–0.076 m, length of horizontal tube H 0.01–0.4 m, length of inclined riser I 0.038–0.6 m and inclination angle of inclined riser θ 40° or 45°.

Wallis-type correlation (J _g ^*1/2+mJ _i ^*1/2=C) was applicable to the data during a steady separated flow. An analysis based on envelope theory showed that the constant C should be a function of H/D and I. A function of C with those parameters was empirically determined by using data obtained in this study. The developed function correlated well with the results of Richter et al. (D = 0.203 m, H = 1.26 m, I = 0.5 m and θ = 45°). The constant m in the Wallis-type correlation was almost constant 0.75. The problems were discussed, which should be made clear to apply the correlation obtained in this study to an actual PWR hot leg.     

Experimental Study on Gas Carry-Under in Down Flow from Two-Phase Mixture

In this paper, simultaneous optimization is carried out for successive two cycles of pressurized water reactors. At first, a simplified problem of the simultaneous optimization was studied by assuming the batch-wise power sharing as independent variable, i.e., batch-wise power sharing was optimized without considering corresponding loading patterns. The optimization of the batch-wise power sharing was carried out for the conventional single cycle, the equilibrium cycle and the two successive (tandem) cycles. The analysis indicated that the tandem cycle optimization well reproduce that of the equilibrium cycle optimization, which is considered as a typical case of the true multicycle optimization. Next, simultaneous optimization of loading patterns for tandem cycles is carried out using the simulated annealing method. Since the design space of the tandem cycles optimization is much larger than that of the conventional single cycle optimization, the optimization condition (i.e., number of calculated patterns) are established through sensitivity study. The optimization results are compared with those obtained by the successive single cycle optimizations and it is clarified that the successive single cycle optimization well reproduces the optimization results obtained by the simultaneous optimization if objective functions are appropriately chosen. The above result will be encouraging for the current in-core optimization method since single cycle optimization is utilized due to limitation of computation time.     

Experimental Study on Gas Carry-Under in Liquid Down Flow from a Two-Phase Mixture

The gas carry-under characteristics in liquid down flow from a two-phase mixture flow have been studied for various flow parameters, based on experiments with a small scale air- water system simulating the concept of a natural circulation BWR with no separators. For high void fraction in the riser, as the liquid superficial velocity jf increased to 0.17 m/s, the void fraction in the lower part of the downcomer αd increased sharply due to the descent of comparatively large bubbles (diameter: about 4–6mm). In the region of jf> 0.17m/s, on increasing jf, the void fraction αd increased until it reached a maximum value at jf.3. For liquid descending velocities higher than 0.3 m/s, αd became almost constant and the level of the mixture above the riser had little effect on the void fraction ad due to the phase separation of the large bubbles formed by bubble coalescence in the upper part of the downcomer. The void fraction αd increased as the void fraction αr increased until bubble coalescence occurred in the upper part of the downcomer, and αd became constant and independent of αr after the occurrence of bubble coalescence. Under the conditions of high void fractions in the riser, 0.4<αr<0.64 (upper limit of the tests), and high liquid descending velocities in the down-comer, 0.3 m/s<jf.<0.4 m/s (upper limit of the tests), the void fraction αd was represented by a dimensionless number (G = η⁴ g/σ³ pf) and by the upper limit of void fractions in bubbly flow, αd=0.3.     

Vold Fraction Correlation for Boiling and Non-Boiling Vertical Two-Phase Flows in Tube

Abstract

Applicability of previously proposed Vold fraction correlation was studied on the boiling steam-water flows in tube. The correlation was found to be applicable to the data of Sekoguchi (d=13.55 mm) and Bartolomei (d=25mm), i.e. the value of parameter K in the correlation equals to unity. The average value of K for pipes of smaller diameter (d= 6.1, 7.7 mm) was 0.57 for both adiabatic and diabatic steam-water flows. These values of k are not dependent on flow regime, heat flux and superficial water velocity within the investigated ranges. A criterion was established with a dimensionless group Eoλ which determines the K-value as: K=1.0 for Eoλ≧2×10⁶ and K=0.57 for Eoλ<2×10⁶.

A comparison between the predicted values by this method and experimental values at pressures from atmospheric to 80 kg/cm² abs., heat fluxes 0–1.5×10⁶ kcal/m²-hr, pipe diameters 5–76.2mm and gas-water volumetric flow ratios 0.06–10⁴, showed that the present correlation is adequate within ±15% of deviation.     

Friction Pressure Drop and Heat Transfer Coefficient of Two-Phase Flow in Helically Coiled Tube Once-Through Steam Generator for Integrated Type Marine Water Reactor

Two-phase friction pressure drop and heat transfer coefficients in a once-through steam generator with helically coiled tubes were investigated with the model test rig of an integrated type marine water reactor. As the dimensions of the heat transfer tubes and the thermal-fluid conditions are almost the same as those of real reactors, the data applicable directly to the real reactor design were obtained. As to the friction pressure drop, modified Kozeki's prediction which is based on the experimental data by Kozeki for coiled tubes, agreed the best with the experimental data. Modified Martinelli-Nelson's prediction which is based on Martinelli-Nelson's multiplier using Ito's equation for single-phase flow in coiled tube, agreed within 30%. The effect of coiled tube on the average heat transfer coefficients at boiling region were small, and the predictions for straight tube could also be applied to coiled tube. Schrock-Grossman's correlation agreed well with the experimental data at the pressures of lower than 3.5 MPa. It was suggested that dryout should be occurred at the quality of greater than 90% within the conditions of this report.