基于竖直圆管空气-水两相流实验的相间曳力模型研究

研究两相流相间阻力特性对系统程序关键本构模型封闭具有重要意义。本文基于竖直圆管开展了空气-水两相流实验,采用四探头电导探针对空泡份额、气泡弦长和界面面积浓度等气泡参数的径向分布进行了测量。结果表明空泡份额和气泡弦长呈现“核峰型”分布,而界面面积浓度并没有表现出随流速的单调关系。进一步开发了泡状流和弹状流的相间曳力模型,考虑了液相表观流速与管径对气泡尺寸分布的影响,建立了临界韦伯数与不同液相流速的关系。计算得到的空泡份额和界面面积浓度与实验数据整体符合较好,验证了模型的可靠性,为两相流相间阻力特性研究提供参考意义。     

Local measurement of interfacial area, interfacial velocity and liquid turbulence in two-phase flow

Double sensor probe and hotfilm anemometry methods were developed for measuring local flow characteristics in bubbly flow. The formulation for the interfacial area concentration measurement was obtained by improving the formulation derived by Kataoka and Ishii. The assumptions used in the derivation of the equation were verified experimentally. The interfacial area concentration measured by the double sensor probe agreed well with one by the photographic method. The filter to validate the hotfilm anemometry for measuring the liquid velocity and turbulent intensity in bubbly flow was developed based on removing the signal due to the passing bubbles. The local void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter, liquid velocity, and turbulent intensity of vertical upward air–water flow in a round tube with an inner diameter of 50.8 mm were measured by using these methods. A total of 54 data sets were acquired consisting of three superficial gas flow rates, 0.015–0.076 m s⁻¹, and three superficial liquid flow rates, 0.600, 1.00, and 1.30 m s⁻¹. The measurements were performed at the three locations: L/D=2, 32, and 62. This data is expected to be used for the development of reliable constitutive relations which reflect the true transfer mechanisms in two-phase flow.     

竖直下降两相流相界面结构输运特性

竖直下降两相流具有与竖直上升两相流不同的相界面结构特征及输运特性。本文对竖直下降管内的气水两相流进行了实验研究,运用微型四头电导探针对7.5、31.5及55.5倍管径横截面处的空泡份额、相界面浓度、气泡直径、气泡频率及气泡速度等相界面结构参数的局部分布进行了测量。分析获得了相界面结构参数的沿程变化规律,并研究了气相表观流速对相界面结构发展的影响及一维相界面结构输运特性。发现竖直下降泡状流的升力指向管中心,导致相界面结构参数基本呈中心峰值分布;气相表观流速的增大会提高空泡份额和相界面浓度分布的峰度;竖直下降两相流在距入口31.5倍管径处基本达到充分发展。     

Void distribution and bubble motion in bubbly flows in a 4×4 rod bundle. Part II: numerical simulation

Numerical simulations of bubbly flows in a four by four rod bundle are carried out using a multi-fluid model to examine effects of the numerical treatment of phase distribution and drag model. The transport equations of bubble number density and void fraction are used as the continuity equation of the gas phase. Two drag models are tested: one of them accounts for the bubble deformation (aspect ratio), whereas the other does not. The rod diameter, the rod pitch and the hydraulic diameter of the rod bundle are 10, 12.5 and 9.1 mm, respectively. The gas and liquid volume fluxes are J_G = 0.06 m/s and J_L = 0.9 and 1.5 m/s, respectively. The bubble diameter ranges from 1 to 5 mm. Comparisons between the numerical and measured data show that (1) the restriction on bubble lateral motion due to the presence of rods can be taken into account by using the transport equation of bubble number density, whereas that of the void fraction cannot deal with the restriction and causes large errors in the distribution of void fraction and (2) the reduction in the bubble-relative velocity near the wall is predictable by using the drag model accounting for the bubble deformation effect.     

Internal structure and interfacial velocity development for bubbly two-phase flow

This paper describes an experimental study of the internal structure of air-water flowing horizontally. The double-sensor resistivity probe technique was applied for measurements of local interfacial parameters, including void fraction, interfacial area concentration, bubble size distributions, bubble passing frequency and bubble interface velocity. Bubbly flow patterns at several flow conditions were examined at three axial locations, L/D = 25, 148 and 253, in which the first measurement represents the entrance region where the flow develops, and the second and third may represent near fully developed bubbly flow patterns. The experimental results are presented in three-dimensional perspective plots of the interfacial parameters over the cross-section. These multi-dimensional presentations showed that the local values of the void fraction, interfacial area concentration and bubble passing frequency were nearly constant over the cross-section at L/D = 25, with slight local peaking close to the channel wall. Although similar local peakings were observed at the second and third locations, the internal flow structure segregation due to buoyancy appeared to be very strong in the axial direction. A simple comparison of profiles of the interfacial parameters at the three locations indicated that the flow pattern development was a continuous process. Finally, it was shown that the so-called “fully developed” bubbly two-phase flow pattern cannot be established in a horizontal pipe and that there was no strong correspondence between void fraction and interface velocity profiles.     

Gas–liquid two-phase flow in narrow horizontal annuli

Experimental data associated with the two-phase flow regimes, void fraction and pressure drop in horizontal, narrow, concentric annuli are presented. Two transparent test sections, one with inner and outer diameters of 6.6 and 8.6 mm, and an overall length of 46.0 cm; the other with 33.2 and 35.2 mm diameters and 43.0 cm length, respectively, were used. Near-atmospheric air and water constituted the gas and liquid phases, respectively. The gas and liquid superficial velocities were varied in the 0.02–57 and 0.1–6.1 m s⁻¹ ranges, respectively. The major two-phase flow patterns observed included bubbly, slug/plug, churn, stratified, and annular. Transitional regimes, where the characteristics of two distinct flow regimes could be observed in the test sections, included bubbly-plug, stratified-slug and annular-slug. The obtained flow regime maps were different than flow regime maps typical of large horizontal channels and microchannels with circular cross-sections. They were also different from the flow regimes in rectangular thin channels. The measured average void fractions for the two test sections were compared with predictions of several empirical correlations. Overall, a correlation proposed by Butterworth [Butterworth, D., 1975. A comparison of some void fraction relationships for co-current gas–liquid flow. Int. J. Multiphase Flow 1, 845–850] based on the results of Lockhart and Martinelli (1949) provided the most accurate prediction of the measured void fractions. The measured pressure drops were compared with predictions of several empirical correlations. The correlation of Friedel [Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. 3R Int. 18, 485–492] was found to provide the best overall agreement with the data.     

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.     

Film boiling heat transfer from a vertical cylinder in forced flow of liquids under saturated and subcooled conditions at pressures

Forced convection film boiling heat transfer on a vertical 3-mm diameter and 180-mm length platinum test cylinder located in the center of the 40-mm inner diameter test channel was measured. Saturated water, and saturated and subcooled R113 were used as the test liquids that flowed upward along the cylinder in the test channel. Flow velocities ranged from 0 to 3 m s⁻¹, pressures from 102 to 490 kPa, and liquid subcoolings for R113 from 0 to 60 K. The heat transfer coefficients for a certain pressure and liquid subcooling are almost independent of flow velocity and of a vertical position on the cylinder for the flow velocities lower than ≈1 m s⁻¹ (the first range), and they become higher for the velocities higher than ≈1 m s⁻¹ (the second range). Slight dependence on a vertical position being nearly proportional to z^−1/4, where z is the height from the leading edge of the test cylinder, exists for the flow velocities in the second range. The heat transfer coefficients at each velocity in the first and second ranges are higher for higher pressure and liquid subcooling. Correlation for the forced convection film boiling heat transfer with radiation contribution on a vertical cylinder was derived by modifying an approximate analytical solution for a two-phase laminar boundary layer model to agree better with the experimental data. It was confirmed that the experimental data of film boiling heat transfer coefficients in water and R113 were described by the correlation within ±20% difference.     

JR curves of the low alloy steel 20 MnMoNi 5 5 with two different sulphur contents in oxygen-containing high temperature water at 240°C

J_R curves of the low alloy steel 20 MnMoNi 5 5 with two different sulphur contents (0.003 and 0.011 wt.%) were determined at 240°C in oxygen-containing high temperature water as well as in air. The tests were performed by the single-specimen unloading compliance technique at load line displacement rates from 1 × 10⁻⁴ down to 1 × 10⁻⁶ mm s⁻¹ on 20% side-grooved 2T CT specimens in an autoclave testing facility at an oxygen content of 8 ppm and a pressure of 7 MPa under quasi-stagnant flow conditions.In the case of testing in high temperature water, remarkably lower J_R curves than in air at the same load line displacement rate (1 × 10⁻⁴ mm s⁻¹) were obtained. A decrease in the load line displacement rate as well as an increase in the sulphur content of the steel caused a reduction of the J_R curves. At the fastest load line displacement rate a stretch zone could be detected fractographically on the specimens tested in air and in high temperature water and consequently J_i could be determined. When testing in high temperature water, the J_i value of the higher sulphur material type decreases from 45 N mm⁻¹ in air to 3 N mm⁻¹, much more than that of the optimized material type from 51 N mm⁻¹ in air to 20 N mm⁻¹ at 1 × 10⁻⁴ mm s⁻¹.     

Investigation of the ductile fracture properties of type 304 stainless steel plate, welds, and 4-inch pipe

J-integral fracture toughness tests were performed on welded 304 stainless steel 2-inch plate and 4-inch diameter pipe. The 2-inch plate was welded using a hot-wire automatic gas tungsten arc process. This weldment was machined into 1T and 2T compact specimens for single specimen unloading compliance J-integral tests. The specimens were cut to measure the fracure toughness of the base metal, weld metal and the heat affected zone (HAZ). The tests were performed at 550°F, 300°F and room temperature. The results of the J-integral tests indicate that the J_Ic of the base plate ranged from 4400 to 6100 in lbs/in² at 550°F. The J_Ic values for the tests performed at 300°F and room temperature were beyond the measurement capacity of the specimens and appear to indicate that J_Ic was greater than 8000 in lb/in². The J-integral tests performed on the weld metal specimens indicate that the J_Ic values ranged from 930 to 2150 in lbs/in² at 550°F. The J_Ic values of the weld metal specimens tested at 300°F and room temperature were 2300 and 3000 in lbs/in² respectively. One HAZ specimen was tested at 550°F and found to have a J_Ic value of 2980 in lbs/in² which indicates that the HAZ is an average of the base metal and weld metal thoughness. These test results indicate that there is a significant reduction in the initiation fracture toughness as a result of welding.The second phase of this task dealt with the fracture toughness testing of 4-inch diameter 304 stainless steel pipes containing a gas tungsten arc weld. The pipes were tested at 550°F in four point bending. Three tests were performed, two with a through wall flaw growing circumferentially and the third pipe had a part through radial flaw in combination with the circumferential flaw. These tests were performed using unloading compliance and d.c. potential drop crack length estimate methods. The results of these test indicate that the presence of a complex crack (radial and circumferential) reduces in the initiation toughness and the tearing modulus of the pipe material compared to a pipe with only a circumferentially growing crack.     

Upward air–water bubbly flow characteristics in a vertical square duct

In nuclear engineering fields, gas–liquid bubbly flows exist in channels with various shape and size cross-sections. Although many experiments have been carried out especially in circular pipes, those in a noncircular duct are very limited. To contribute to the development of gas–liquid bubbly flow model for a noncircular duct, detail measurements for the air–water bubbly flow in a square duct (side length: 0.136 m) were carried out by an X-type hot-film anemometry and a multi-sensor optical probe. Local flow parameters of the void fraction, bubble diameter, bubble frequency, axial liquid velocity and turbulent kinetic energy were measured in 11 two-phase flow conditions. These flow conditions covered bubbly flow with the area-averaged void fraction ranging from 0.069 to 0.172. A pronounced corner peak of the void fraction was observed in a quarter square area of a measuring cross-section. Due to a high bubble concentration in the corner, the maximum values of both axial liquid velocity and turbulent kinetic energy intensity were located in the corner region. It was pointed out that an effect of the corner on accumulating bubble in the corner region changed the distributions of axial liquid velocity and turbulent kinetic energy intensity significantly.     

Numerical investigation of boiling regime transition mechanism by a Lattice–Boltzmann model

A numerical study has been performed to investigate the hydrodynamic aspects of the pool boilingon horizontal-, vertical- and downward-facing surfaces. The FlowLab code, which is based on a Lattice–Boltzmann (LB) model of two-phase flows, is employed. Macroscopic properties, such as surface tension (σ) and contact angle (β), are implemented through the fluid–fluid (G_σ) and fluid–solid (G_t) interaction potentials. The model is found to express a linear relation between the macroscopic properties (σ, β) and microscopic parameters (G_σ, G_t). The simulation results on bubble departure diameter appear to have the same parametric dependence as the empirical correlation. Hydrodynamic aspects of two-phase flow regime transition mechanism are investigated for different surface–coolant configurations. Results of the LB simulation clearly demonstrate that not only the bubble nucleation site density (related, e.g. to the heater surface condition and heat fluxes), but also the surface position have a profound effect on the flow regime (pool boiling) characteristics. The results of the LB simulation of hydrodynamics of two-phase flow on the horizontal surface provide the pictures quite similar to the experimental observation for saturated pool boiling. Two mechanisms of flow (boiling) regime transition on the vertical surface are predicted for the local bubble coalescence at bubble generation site and the downstream bubble coalescence. On the downward-facing surfaces, friction between bubbles and the surface wall is found to significantly enlarge the bubble size prior the bubble slip upwards. This behavior is responsible for the earlier bubble coalescence, and therefore, lowers the maximum heat removal rate, in a similar regime of nucleate boiling on a downward-facing surface.     

Basic Studies on Two-Phase Flow with the Use of Electrical Void-Meter

Further basic knowledge has been gained on the behavior of two-phase flow through the following experiments. An electrical void-meter based on transducement of void fraction into impedance is employed to measure the void distribution along a heater in an annular channel.

Experiments have further been conducted on the “velocity slip ratio (V_g/V₁)” to correlate the void-fraction (R_g,) with the volume flow rate ratio (F_g). The resulting equation takes the form R_g= 0.92-F_g and the ratio V_g/V_g= 1.08, for slug flow in a vertical pipe.

Statistical methods have been applied in analyzing the two-phase flow. It is shown that the speed of voids in a two-phase flow can be determined with a cross-correlation function calculated from two time series of void-fraction fluctuation measured at two points along the channel.     

Distribution parameter and drift velocity for two-phase flow in a large diameter pipe

In view of practical importance of the drift flux model for two-phase flow analysis in general, and in the analysis of nuclear reactor transients and accidents in particular, the distribution parameter, and the drift velocity have been studied for two-phase flow in a vertical large diameter pipe. In this, study, local measurements were performed on flow parameters, such as void fraction, gas velocity and, liquid velocity in a vertical upward air–water two-phase flow in a pipe of 200 mm inner diameter and, 25 m in height by using the local sensor techniques such as hot-film probes, optical multi-sensor, probes and differential pressure gauges. Two-phase flow regimes in a vertical large diameter pipe, were classified into bubbly, churn and slug flows according to the visual observation. The values of the, distribution parameter and the mean drift velocity were determined directly by their definition using experiment data of the local flow parameters in a two-phase flow in a large diameter pipe. Various existing drift flux correlations were compared with the present experimental results and experimental data obtained by other researchers. A detailed discussion on the problems of these correlations was presented in this paper.     

Visualization and measurement of two-phase flow by using neutron radiography

To apply neutron radiography (NR) technique to fluid research, high frame-rate NR with a steady thermal neutron beam has been developed in the present research program by assembling up-to-date technologies for neutron source, scintillator, high-speed video and image intensifier. This imaging system has many advantages such as a long recording time (up to 21 min), high-frame-rate (up to 1000 frames s⁻¹) imaging and no need for triggering signal. Visualization of air-water two-phase flow in a metallic duct was performed at the recording speeds of 250, 500 and 1000 frames s⁻¹. The qualities of those consecutive images were good enough to observe and measure the flow structure and the characteristics. It was demonstrated also that some characteristics of two-phase flow could be measured by using the present imaging system. Image processing technique enabled measurements of various flow characteristics in two ways. By utilizing geometrical information extracted from NR images, data on flow regime, rising velocity of bubbles, and wave height and interfacial area in annular flow were obtained. By utilizing attenuation characteristics of neutrons in materials, measurements of void profile and average void fraction were performed. It was confirmed that this new technique may have significant advantages both in visualizing and measuring high-speed fluid phenomena when the other methods such as an optical method and X-ray radiography cannot be applicable.     

Experimental and numerical investigation of counter-current stratified flows in horizontal channels

Counter-current flow regimes of air and water are investigated in the WENKA test facility at the Forschungszentrum Karlsruhe. With the fluorescent-particle image velocimetry (PIV) measurement technique, velocity and velocity fluctuations are measured up to the free surface. A statistical model is presented to correlate the measured void fraction with the turbulent kinetic energy calculated from the measured velocity fluctuations. The experimental data are used to develop a phase interaction model to simulate stratified flows. Two different approaches are compared for turbulence modelling. The Prandtl mixing length model and an extended k–ω model for the two-phase region are applied to supercritical flow conditions.     

Non-stationary outflow and rarefaction waves in flashing liquid

The outflow of high pressure liquid (in particular, water) to the atmosphere from a closed tube (of length a few metres and diameter more than a few centimetres) because of sudden destruction of one bottom is theoretically investigated. Evaporation takes places on the nucleus bubbles. The number of nuclei depends on the quality of the liquid or its purification. The process involves flashing evaporation of the liquid.There are two rarefaction waves at the initial stage. The velocity of the first wave (elastic forerunner) is sound speed in the one phase liquid and equals about 1000 m s⁻¹. After the elastic forerunner the liquid becomes superheated because the pressure drops and evaporation begins.The velocity of the second rarefaction wave is about 1–10 ms s⁻¹. There is intensive bubbly evaporation on and after the second wave. Intensity of the outflow is determined by the intensity of evaporation on the interface of the bubbles and by intensity of fragmentation of the bubbles because of their relative slip velocity in the liquid (0.1–1 m s⁻¹). The fragmentation of the bubbles significantly intensifies the evaporation because of augmentation of the bubbly interface.The degree of non-equilibrium or superheating behind the forerunner in water grows with the increasing initial temperature T₀. For T₀<530−540 K this superheating is negligible and the process may be described by an equilibrium scheme. For T₀ above 0.95T_cr≈605 K homogeneous nucleation is possible.After forerunner reflection from the closed bottom, intense evaporation is initiated near the bottom. Then the equalization of the pressure along the tube occurs (quasi-static homobaric stage).There is good correlation with experimental data.     

Upward vertical two-phase flow local flow regime identification using neural network techniques

Traditionally, the flow regimes in two-phase flow are considered in a global sense. However, a local flow regime is required to understand and model the interfacial structures present in the flow. In this work, a new approach has been used to identify both global and local flow regimes in a two-phase upward flow in a 50.8 mm internal diameter pipe under adiabatic conditions. In the present method, the bubble chord length distributions, which are measured simultaneously with three double-sensor conductivity probes, have been used to feed a self-organized neural network. The global flow regime identification results show a reasonable agreement with the visual observation for all the flow conditions. Nonetheless, only the local flow regimes measured at the center of the pipe agree with the global ones. The local flow regime combinations found are analyzed using the flow map information, cross-correlations between the probe signals, and previous correlations. In this way, it is possible to identify eight different global flow regime configurations.     

Gas–liquid flow around an obstacle in a vertical pipe

This paper presents a novel technique to study the two-phase flow field around an asymmetric obstruction in a vertical pipe with a nominal diameter of DN200. Main feature of the experiments is the shifting of a half-moon shaped diaphragm causing the obstruction along the axis of the pipe. In this way, the 3D void field is scanned with a stationary wire-mesh sensor that supplies data with a spatial resolution of 3 mm over the cross-section and a measuring frequency of 2.5 kHz. Besides the measurement of time-averaged void fraction fields and bubble-size distributions, novel data evaluation methods were developed to extract estimated liquid velocity profiles as well as lateral components of bubble velocities from the wire-mesh sensor data. The combination of void fraction fields and velocity profiles offer the opportunity to analyse a two-phase flow in a geometry that owns a series of features characteristic for complex components of power and chemical plant equipment. Such characteristics are sharp edges with flow separation, recirculation areas, jet formation, stagnation points and curved stream-lines.

The tests were performed with an air–water flow at nearly ambient conditions and with a saturated steam–water mixture at 6.5 MPa. The superficial velocities of liquid and gas or, respectively, vapour were varied in a wide range.

The flow structure upstream and downstream of the obstacle is characterized in detail. Bubble size dependent effects of bubble accumulation and migration are discussed on basis of void-fraction profiles decomposed into bubble-size classes. A pronounced influence of the fluid parameters was found in the behaviour of bubbles at the boundary of the jet coming from the non-obstructed part of the cross-section. In case of an air–water flow, bubbles are restrained from entering the jet, a phenomenon which was not observed in high-pressure steam–water flow. A detailed uncertainty analyse of the velocity assessments finishes the presented paper. A blind pre-test calculation with CFX-10 based on the assumption of a mono-disperse bubbly flow has reproduced the overall void and velocity profiles. The results are used for the assessment of the influence of local accelerations on the liquid velocity measurement.     

Interfacial measurements in horizontal stratified flow patterns

The interfacial characteristic parameters of horizontal stratified wavy flow patterns were experimentally investigated for a mixture of air and water two-phase flow by using the double-sensor, parallel wire conductance probe method. The experiments were conducted in a horizontal flow loop 15.4 m long consisting of Pyrex glass tubing of 50.3 mm i.d. The range of gas superficial velocities was from 0.85 to 31.67 ms⁻¹ and the liquid superficial velocities ranged from 0.014 to 0.127 ms⁻¹. Several interfacial wave patterns as described by Andritsos and Hanratty (Int. J. Multiphase Flow 13 (1987a) 583–603) were identified and their characteristic parameters such as wave height, most dominant frequency, mean propagation velocity and mean wavelength were investigated in terms of liquid and gas flow rates. The interfacial shear stress calculated from the experimental measurements was used to evaluate the most widely used interfacial shear models.