Irreversible pressure losses in two-phase flow systems

An energy rate method is used to derive an equation for the irreversible pressure loss in two-phase flow. The pressure loss is found to be a function of the components' density, viscosity, quality, and the slip ratio or cross-sectional area fraction of the vapor; covers the entire quality range; and reduces to the proper equation for one-phase flow. The equation has a trend similar to the Martinelli-Nelson curve, but modifications have been incorporated to fit it to data with more accuracy. The equation, evaluated for steam-water, provides a method for calculation of interfacial losses and the individual losses in the vapor and liquid. Refitting of two factors to data is expected to allow extension to other two-phase, one-component flows, or to two-phase, two-component flows.     

Scaling laws for thermal-hydraulic system under single phase and two-phase natural circulation

Scaling criteria for a natural circulation loop under single phase and two-phase flow conditions have been derived. For a single phase case the continuity, integral momentum, and energy equations in one-dimensional area average forms have been used. From this, the geometrical similarity groups, friction number, Richardson number, characteristic time constant ratio, Biot number, and heat source number are obtained. The Biot number involves the heat transfer coefficient which may cause some difficulties in simulating the turbulent flow regime. For a two-phase flow case, the similarity groups obtained from a perturbation analysis based on the one-dimensional drift-flux model have been used. The physical significance of the phase change number, subcooling number, drift-flux number, friction number are discussed and conditions imposed by these groups are evaluated. In the two-phase flow case, the critical heat flux is one of the most important transients which should be simulated in a scale model. The above results are applied to the LOFT facility in case of a natural circulation simulation. Some preliminary conclusions on the feasibility of the facility have been obtained.     

Local two-phase flow measurements using sensor techniques

Radial profiles of various local parameters in bubbly two-phase flow were obtained. Measurements of the local void fraction, the local interfacial area concentration, the bubble interfacial velocity and Sauter mean diameter were made using the double sensor probe method. At the same locations, local liquid velocity and turbulence intensity measurements were made using a hotfilm anemometer. Data was taken at three different axial locations (L/D=2, L/D=32 and L/D=62) along a 3.24 m test section with an inner diameter of 0.0508 m. In comparison to previous data sets, the following data is more complete in the sense that both interfacial area measurements are combined with one of the local driving forces for interfacial transfer, namely the liquid turbulent diffusion. There have been few, if any, studies done combining local liquid turbulence and the local interfacial area concentration. The data taken will eventually be applied to the closure relations required by the one-dimensional, time-averaged interfacial area transport equation.     

Frictional pressure drop of gas liquid two-phase flow in pipes

Experiments of air water two-phase flow frictional pressure drop of vertical and horizontal smooth and relatively rough pipes were conducted, respectively. The result demonstrated that the frictional pressure drop increases with increasing relative roughness of the pipe. However, the influence of the relative roughness becomes more evident at higher vapour quality and higher mass flux. A new prediction model for frictional pressure drop of two-phase flow in pipes is proposed. The model includes a new definition of the Reynolds number and the friction factor of two-phase flow. The proposed model fits the presented experimental data very well, for vertical, horizontal, smooth and rough pipes. Therefore, the reproductive accuracy of the model is tested on the experimental data existing in the open literature and compared with the most common models. The statistical comparison, based on the Friedel’s Data-Bank containing of about 16,000 measured data, demonstrated that the proposed model is the best overall agreement with the data. The model was tested for a wide range of flow types, fluid systems, physical properties and geometrical parameters, typically encountered in industrial piping systems. Hence, calculating based on the new approach is sufficiently accurate for engineering purposes.     

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.     

Numerical study of nuclear coupled two-phase flow instability in natural circulation system under low pressure and low quality

Based on the one-dimension two-phase drift flow model, the numerical simulation of two-phase flow stability characteristic on the test loop (HRTL-5) for 5 MW heating reactor (developed by the Institute of Nuclear and New Energy Technology of Tsinghua University, Beijing) is performed with and without coupled point neutron kinetics. The density wave oscillation instability is analyzed in the system under low pressure at 1.5 MPa and low steam quality less than 10%. The effect of inlet subcooling and heating flux on the system instability is simulated under the system pressure P_sys = 1.5 MPa. The numerical results show that there exist two instability inlet subcooling boundaries at different heat flux. The numerical results show good agreement with the experimental results on HRTL-5 without consideration of point neutron kinetics. If coupled with point neutron kinetics, the system will exhibit little difference on instability boundaries from that without considering the nuclear characteristics. But the amplitude and the phase of the oscillation of the thermal hydraulic parameters of the system will be somehow affected in unstable zone if the system is coupled with point neutron kinetics.     

Analysis of flow induced valve operation and pressure wave propagation for single and two-phase flow conditions

The flow induced valve operation is calculated for single and two-phase flow conditions by the fluiddynamic computer code DYVRO and results are compared to experimental data. The analysis show that the operational behaviour of the valves is not only dependent on the condition of the induced flow, but also the pipe flow can cause a feedback as a result of the induced pressure waves. For the calculation of pressure wave propagation in pipes of which the operation of flow induced valves has a considerable influence it is therefore necessary to have a coupled analysis of the pressure wave propagation and the operational behaviour of the valves.The analyses of the fast transient transfer from steam to two-phase flow show a good agreement with experimental data. Hence even these very high loads on pipes resulting from such fluiddynamic transients can be calculated realistically.     

Type of flow, pressure drop, and critical heat flux of a two-phase sodium flow

Little is known about the two-phase pressure loss, the flow pattern, and the critical heat flux conditions for boiling sodium under forced convection. The specific thermohydraulic properties of sodium prohibit extrapolation to sodium of experimental data obtained for other liquids. Therefore, some new test series were carried out in a sodium loop with an induction heated test section of 9 mm inner diameter and 200 mm heated length. The two-phase pressure loss and the film thickness were measured up to the critical cooling conditions. The experimental results are compared with values predicted by known models on annular flow and annular mist flow, respectively. Satisfactory predictions of the flow pattern and the critical heat flux conditions could only be obtained using the measured two-phase pressure losses.     

Correlations for predicting single phase and two-phase flow pressure drop in pebble bed flow channels

An experimental study was conducted on the pressure drop of the single phase and the air–water two-phase flow in the bed of rectangular cross sections densely filled with uniform spheres. Three kinds of glass spheres with different equivalent diameters (3 mm, 6 mm, and 8 mm) were used for the establishment of the test sections. The Reynolds number in the experiment ranged from a dozen to thousands for the single-phase flow and from hundreds to tens of thousands for the two-phase flow. In the present flow-regime model, the bed was subdivided into a near-wall region and a central region in order to take the wall effect into account to improve the prediction at low tube-to-particle diameter ratios. Improved correlations are obtained based on the previous study to consider the single-phase flow pressure drops for finite pebble beds with spherical particles and nonspherical particles by fitting the coefficients of that equation to both the database and the present experiment. The correlation is consistent with the observed physical behavior which explains its comparatively good agreement with the experimental data. A new empirical correlation for the prediction of two-phase flow pressure drops was proposed based on the gas phase relative permeability as a function of the gas phase saturation and the void fraction. The correlation fit well for both experimental data of spherical particles and nonspherical particles.     

Flow regime identification using chaotic characteristics of two-phase flow

Chaotic nature of two-phase flow is investigated for its dependency upon the flow regime by constructing the pseudo phase space with the time sequential impedance signals of the void fraction. In order to construct the pseudo phase space, the autocorrelation function (ACF) and the average mutual information (AMI) for the delayed time, and the false nearest neighborhood (FNN) for the dimensions as the embedding parameters were employed here. It was found that the delayed time and embedded dimension are highly dependent upon the flow regime. To visualize the trajectory of signals in the phase space, a density map is produced by the projection of the trajectory into the two-dimensional plane which is correspondent with the two-dimensional probability distribution functions (2D-PDF). Since the density map of 2D-PDF showed clear distinction of flow patterns, we developed a method to identify flow regime by applying simple classification rules to the density map. The proposed method successfully identifies the flow regimes of the experimental data of impedance signals for the void fraction produced flow regime map for the vertical channel with diameter of 25.4 and 50.8 mm.     

Vertical two-phase flow identification using advanced instrumentation and neural networks

Most two-phase flow measurements, including void fraction measurements, depend on correct flow regime identification. There are two steps taken towards the successful identification of flow regimes: first, develop a non-intrusive instrument to demonstrate area-averaged void fluctuations and second, develop a non-linear mapping approach to perform objective identification of flow regimes. In this paper, an advanced non-intrusive impedance void-meter provides input signals to neural networks which are used to identify flow regimes. After training, both supervised and self-organizing neural network learning paradigms performed flow regime identification successfully. The methodology presented holds considerable promise for multiphase flow diagnostic and measurement applications.     

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.     

An analysis of multidimensional reactor transients using reduced integration techniques in the finite-element method

New finite-element formulations based on numerical integration of mass and stiffness matrices have been used for solving the time-dependent multigroup diffusion theory equations in multidimensions. There is a drastic reduction in the coupling of the nodal unknowns. This facilitates the use of a fast and stable time integration scheme, viz. an alternating-direction explicit (ADE) algorithm. Frequency transformation is used to limit the truncation error due to temporal differencing. This model is incorporated in a code called fintran. Analyses of 2-D and 3-D reactor transients indicate that the present method can be as efficient as other fast nodal methods.     

A study of two-phase flow characteristics using reactor noise techniques

Recent work at the University of Washington has demonstrated the potential for studying two-phase flow characteristics using neutron noise techniques. This method offers the advantage of measuring global characteristics of two phase phenomenon without disturbing the flow or requiring large numbers of sensors. Not only can the presence of the injected air into the flow loops be seen in the neutron spectrum but also the neutron spectrum reflects the type of flow by producing a characteristic signature.     

Wave propagation in two-phase flow of magnetic fluid under a nonuniform magnetic field

The effect of nonuniform magnetic field on the linear and nonlinear wave propagation phenomena in two-phase pipe flow of magnetic fluid is investigated theoretically to realize the effective energy conversion system using boiling two-phase flow of magnetic fluid. Firstly, the governing equations of two-phase flow based on the unsteady thermal nonequilibrium two-fluid model are presented and the linear void wave propagation phenomena in boiling two-phase flow are numerically analyzed by using the finite volume method. Next, the nonlinear pressure wave propagation in gas-liquid two-phase flow is numerically analyzed by using the finite different method. According to these theoretical studies on the wave propagation phenomena in two-phase flow of magnetic fluid, it seems to be a reasonable proposal that the precise control of the wave propagation in two-phase flow is possible by effective use of the magnetic force.     

Flooding and flow reversal of two-phase annular flow

The flooding and flow reversal conditions of two-phase annular flow are mathematically defined in terms of a characteristic function representing a force balance. Sufficiently below the flooding point in counter-current flow, the interface is smooth and the characteristic equation reduces to the Nusselt relationship. Just below the flooding point and above the flow reversal point in cocurrent flow, the interface is “wavy”, so that the interfacial shear effect plays an important role. The theoretical analysis is compared with experimental results by others. It is suggested that the various length effects which have been experimentally observed may be accounted for by the spatial variation of the droplet entrainment.     

Modeling and analysis of hydrodynamic instabilities in two-phase flow using two-fluid model

Because of the practical importance of two-phase flow instabilities, especially in boiling water nuclear reactor technology, substantial efforts have been made to date to understand the physical phenomena governing such instabilities and to develop computational tools to model the dynamics of marginally-stable/unstable boiling systems. The purpose of this paper is to present an integrated methodology for the analysis of flow-induced instabilities in boiling channels and systems. The major novel aspects of the proposed approach are: (a) it is based on the combined frequency-domain and time-domain methods, the former used to quantify stability margins and to determine the onset of instability conditions, the latter to study the nonlinear system response outside the stability boundaries identified using the nearly-exact results of the frequency-domain analysis; (b) the two-fluid model of two-phase flow has been used for the first time to analytically derive the boiling channel transfer functions for the parallel-channel and channel-to-channel instability modes. In this way, the major characteristics of a boiling system, including the onset-of-instability conditions, can be readily evaluated by using the qualitative frequency-domain approach, whereas the explicit time-domain integration is performed, if necessary, only for the operating conditions that have already been identified as unstable. Both methods use the same physical two-fluid model that, in one case, is linearized and used to derive a rigorous analytical solution in the complex domain, and, in the other case, is solved numerically using an algorithm developed especially for this purpose. The results using both methods have been compared against each other and extensively tested. The testing and validation of the new model included comparisons of the predicted steady-state distributions of major parameters and of the transient channel response against experimental data.     

Theoretical investigations on two-phase flow instability in parallel multichannel system

In this paper, the behavior of multichannel system two-phase flow instability is studied theoretically. A physics model that includes the entrance section, heater section and riser section is built. The subcooled boiling is also included. The results of twin-channel system are compared with the twin-channel experiment. Then the model is extended to the multichannel systems that have more channels. The two-phase flow instability between multichannels (FIBM) is studied under different system pressures, different inlet resistance coefficients and asymmetric heating. The instability boundaries of the multichannel system are obtained in the parameter plane of the subcooling and phase change numbers. A concept of instability space or instability reef is brought forward. Finally, the influence of inlet and riser sections on the FIBM is analyzed.