Interfacial area transport of vertical upward bubbly two-phase flow in an annulus

In relation to the development of the interfacial area transport equation in a subcooled boiling flow, the one-dimensional interfacial area transport equation was evaluated by the data taken in the hydrodynamic separate effect tests without phase change, or an adiabatic air-water bubbly flow in a vertical annulus. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. Twenty data sets consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s were used for the evaluation of the one-dimensional interfacial area transport equation. The one-dimensional interfacial area transport equation agreed with the data with an average relative deviation of ±8.96%. Sensitivity analysis was also performed to investigate the effect of the initial bubble size on the interfacial area transport. It was shown that the dominant mechanism of the interfacial area transport was strongly dependent on the initial bubble size.     

Interfacial friction factor in vertical upward gas-liquid annular two-phase follow

This paper presents new data on the gas-liquid interfacial friction factor in annular two-phase upward co-current flow in a vertical circular pipe. Different from most previous work, the present studies have been performed at relatively high film thickness, taking into consideration the effect of the entrained droplets which occur from the breakup of the disturbance waves. The test section has an inner diameter of 29 mm and the length of 3 m. The porous wall injector is used to introduce the liquid into the test section. The two phase pressure drop is measured by two static pressure tubes connected with a manometer. The film thickness is measured by calibrated stainless ring electrodes mounted flush in the tube wall. The electrode operates on the principle of the variation of electrical resistance with changes in the liquid film thickness between two parallel eletrode rings. The entrained liquid flow rate is measured by using a sampling probe connected with a cyclone separator. The entrainment flow rate in the gas core is calculated from an assumption that the sampling is carried out in an isokinetic manner. The results from the experiments are compared with those calculated from correlations reported in the literature. A new empirical correlation for predicting the interfacial friction factors for practical applications is proposed.     

Liquid film behavior in annular two-phase flow under flow oscillation conditions

Experiments were carried out to investigate the effects of sinusoidal forced oscillation of the inlet flow rate on the time variations of local liquid film thickness and the frequencies of large wave’s passing in steam–water annular two-phase flows. The liquid film thickness oscillated with the same period as the inlet flow rate. The mean film thickness in the thin film regions decreased and approached to an asymptotic value with an increase in the oscillation period of the inlet flow rate. This result was consistent with the experimental results of the occurrence of liquid film dryout under flow oscillation conditions reported in the literature. It was hence considered that the axial liquid transport from the thick to thin film regions mitigates the reduction of the critical heat flux caused by the flow oscillation. It was also found that the wave frequency in the thin film region increased with a decrease in the oscillation period. This observation suggested that the disturbance waves contribute to the enhancements of the liquid transport and consequently the critical heat flux associated with the liquid film dryout under flow oscillation conditions.     

Thermal-hydraulic analysis of the two-phase annular flow under microgravity

The design of the two-phase flow loops applied for thermal control systems of future spacecraft requires knowledge of two-phase flow and heat transfer phenomena under microgravity conditions. This paper deals with a fundamental approach for evaporators or cold plates in two-phase flow loops. A straight evaporator tube was mathematically modeled as a simplified thermal configuration of the cold plate. Simultaneous ordinary differential equations for the two-phase annular flow under microgravity conditions were derived from the separated flow model, and numerical analyses were conducted for the purpose of parametric studies. As a result, properties' distribution of the working fluid along the flow direction, critical limits of the working conditions, and the thermal performance difference owing to the working fluids were clarified. © 1999 Scripta Technica, Heat Trans Asian Res, 29(1): 45–58, 2000     

New entrainment rate correlation in annular two-phase flow applicable to wide range of flow condition

Assuming the rate of droplet entrainment is characterized by the ratio of the interfacial shear force to the surface tension force acting on the phase interface, new correlation representing the rate of droplet entrainment in annular-dispersed two-phase flow was developed. Although the correlation is based on the simple assumption, the quasi-equilibrium droplet flow rates measured in many experiments were predicted reasonably well (root mean square error of entrainment fraction was roughly halved comparing with several existing correlations). Its applicability to the non-equilibrium situation was also demonstrated by the numerical calculations using a one-dimensional three-fluid model.     

Heat- mass transfer and flow characteristics of two-phase countercurrent annular flow in a vertical pipe

Experimental and theoretical results on flow, heat and mass transfer characteristics for the countercurrent flow of air and water in a vertical circular pipe are compared. An experimental setup was designed and constructed. Hot water is introduced through a porous section at the upper end of a test section and flows downward as a thin liquid film on the pipe wall while the air flows countercurrently. The air and water flow rates used in this study are those before the flooding is reached. A developed mathematical model is separated into three parts: A high Reynolds number turbulence model, in which the local state of turbulence characteristics consists of the turbulent kinetic energy (k) and its dissipation rate (ϵ).The transport equations for both k and s are solved simultaneously with the momentum equation to determine the kinetic turbulence viscosity, the pressure drop, interfacial shear stress and then the friction factor at the film/core interface; Heat and mass transfer models are proposed in order to estimate the distribution of the temperature and the mass fraction of water vapor in gas core. The results from the model are compared with the present experimental ones. It can be shown from the present study that the influence of the interfacial wave phenomena is significant to the pressure loss, and the heat and mass transfer rate in the gas phase.     

An improved numerical model for annular two-phase flow with liquid entrainment

The development of a transient numerical model to predict the characteristics of annular two-phase flow with entrainment is presented and discussed. The mathematical formulation of this model is based on finite volume mass, momentum and energy balances. Several constitutive relations are employed to describe the fluid-gas and entrainment interactions. Numerical results indicate that this model present a significant improvement over other existing models in predicting the annular flow characteristics.     

Determining the two-phase friction coefficient in the transition between annular and fog flow

The dependence of the transition conditions between annular and fog flow on the parameters of a system with boiling flow are analysed in order to extend the applicability of a physical model of the two-phase flow recently proposed by the authors to calculate the friction coefficient. Having suitably represented the phenomenon, examination is made as to its influence on the analytical development of the model, the results obtainable from the latter being compared with those of the relations usually employed and with experimental indications, thus showing the broad field of validity of the formulae presented.     

Volumetric interfacial area prediction in upward bubbly two-phase flow

In two-phase flow studies, a volumetric interfacial area balance equation is often used in addition to the multidimensional two-fluid model to describe the geometrical structure of the two-phase flow. In the particular case of bubbly flows, numerous works have been done by different authors on the subject. Our work concerns two main modifications of this balance equation: (1) new time scales are proposed for turbulence induced coalescence and breakup, (2) modeling of the nucleation of new bubbles on the volumetric interfacial area. The 3D module of the CATHARE code is used to evaluate our new model, in comparison to three other models for interfacial area found in the literature, on two different experiments. First, we use the DEBORA experimental data base for the comparison in the case of boiling bubbly flow. The comparison of the different volumetric interfacial area models to the DEBORA experimental data shows that even though the theoretical values of the coefficients are adopted in our modified model, this model has a quite good capability to predict the local two-phase geometrical parameters in the boiling flow conditions. Secondly, we compare the predictions obtained with the same models to the DEDALE experimental data base, for the case of adiabatic bubbly flow. In comparison to the other models tested, our model also gives quite good predictions of the bubble diameter in the case of adiabatic conditions.     

Interfacial friction factors in countercurrent stratified two-phase flow in a nearly-horizontal circular pipe

The interfacial shear stresses for a countercurrent stratified two phase flow in a nearly horizontal circular pipe were determined from a momentum balance using gas and liquid flow rates, wall shear stresses and liquid holdups. The interfacial shear stresses were approximated to be a function of interfacial friction factors, gas and liquid velocities. An empirical correlation for predicting the interfacial friction factors has also been developed for practical applications.     

Experimental and theoretical analysis of annular two-phase flow regimen in direct steam generation for a low-power system

This study aims to quantify and to model the temperature profile around an absorber tube of a parabolic trough concentrator with low fluid flow. This study was specifically developed for the solar power plant of the Engineering Institute, National University of Mexico. This work presents experimental results under saturated conditions and low pressures (1.5–3 bar) using water as the thermal and working fluid for direct steam generation (DSG). The control variable was feed flow. Solar irradiance was used as the restriction variable because all experimental tests should be developed under very specific values of this variable (for example, I > 700 W/m²). The objective of this experiment was to study the thermal behavior of a temperature gradient around the absorber tube under steady-state conditions and with low flow. Additionally, a theoretical analysis was carried out by means of the homogeneous heat conduction equation in the cylindrical coordinate system using only two dimensions (r, ). The finite-difference numerical method was used with the purpose of proposing a solution and obtaining a temperature profile. The objective of this theoretical analysis was to complement the experimental tests carried out for direct steam generation (DSG) with annular two-phase flow patterns for low powers in parabolic trough concentrators with carbon steel receivers.     

The effects of the number and angle of microgrooves on the liquid film in horizontal annular two-phase flow

Measurements of the liquid film profile and pressure drop were made in tubes with grooves of varying angle (0°, 9° and 18°) as well as tubes with varying numbers of grooves at a common angle (18°). These data indicate that the grooves act to redistribute the liquid film on the inner wall perimeter and that only a relatively small number of grooves (12) is needed to do this. The grooves also affect the stability of the vapor-liquid interface and can generate lower average liquid film thickness. The pressure loss is directly related to the number of grooves for the tubes studied.     

Stability of annular flow

A simple transient model using an unsteady state continuity equation and a quasi steady momentum equation is used to analyse the stability of co-current and counter-current annular flows. It is shown that unstable steady state solutions may take place in both cases. Application of the theory is demonstrated for the problem of flooding and flow reversal.     

Prediction of evaporation heat transfer coefficient based on gas–liquid two-phase annular flow regime in horizontal microfin tubes

A physical model of gas–liquid two-phase annular flow regime is presented for predicting the enhanced evaporation heat transfer characteristics in horizontal microfin tubes. The model is based on the equivalence of a periodical distortion of the disturbance wave in the substrate layer. Corresponding to the stratified flow model proposed previously by authors, the dimensionless quantity Fr₀ = G/[gd_eρ_v(ρ_l ? ρ_v)]^0.5 may be used as a measure for determining the applicability of the present theoretical model, which was used to restrict the transition boundary between the stratified-wavy flow and the annular/intermittent flows. Comparison of the prediction of the circumferential average heat transfer coefficient with available experimental data for four tubes and three refrigerants reveals that a good agreement is obtained or the trend is better than that of the previously developed stratified flow model for Fr₀ > 4.0 as long as the partial dry out of tube does not occur. Obviously, the developed annular model is applicable and reliable for evaporation in horizontal microfin tubes under the case of high heat flux and high mass flux.     

Experimental study on interfacial area transport in vertical upward bubbly two-phase flow in an annulus

In relation to the development of the interfacial area transport equation, axial developments of local void fraction, interfacial area concentration, and interfacial velocity of vertical upward bubbly flows in an annulus with the hydraulic equivalent diameter of 19.1 mm were measured by the double-sensor conductivity probe. A total of 20 data were acquired consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. The obtained data will be used for the development of reliable constitutive relations, which reflect the true transfer mechanisms in subcooled boiling flow systems.     

沸腾两相流动中的动力学特征量

采用频域和相空间方法分析沸腾两相流系统。用实测的声压信号重构相空间，并用最大Lyapunov数和相关维数对重构的相空间进行量化。分析这些量化参数与实际实验过程中观察到的流型变化之间的关系。结果表明：声压信号的功率谱和相空间的量化参数均与沸腾流体中的流型变化有关，有可能作为流型变化的特征参量。     

Traveling void wave in horizontal two-phase flow

In the framework of pattern dynamics approach, the discrete bubble model was developed for simulating inherent fluctuation of void fraction in a horizontal two-phase flow. Then flow patterns were identified based on the statistical properties of void fraction fluctuation, and the flow pattern map agreed with the experimental observation of high-pressure two-phase flow of CO₂ in horizontal tubes. The time-averaged pressure drop and the void fraction obtained in the simulation agreed reasonably with the existing correlations. Thus the horizontal flow version of the discrete bubble model demonstrates its relevance in simulating inherent fluctuation of two-phase flow.