Comparisons of the RETRAN two-phase flow model with experimental data

The RETRAN computer program was designed for thermal-hydraulic analysis of nuclear steam supply systems at steady-state and off-normal conditions. A homogeneous equilibrium mixture model (HEMM) of two-phase flow is used in the program. The constitutive models for wall friction, two-phase friction multiplier, heat transfer coefficient, and critical heat flux are compared with steady-state experimental data in this report. The void fraction predicted by the HEMM is also compared with data. The results of the data comparisons indicate that the constitutive models are accurate representations and that the RETRAN numerical scheme provides an excellent framework for data comparisons.     

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

A differential model for adiabatic, fully developed, annular two-phase flow with liquid entrainment has been developed. The model is based on a modified form of the single-phase mixing length function to account for turbulence intensity attenuation due to the presence of entrained liquid droplets in the gas core. Simultaneous predictions of pressure drop and average film thickness for given flow rates show good agreement with a wide range of experimental results for various fluids at several pressures in a range of tube diameters for both horizontal and vertical (upwards and downwards) flows.     

Post-CHF two-phase flow with low wall-superheat

Heat transfer was measured to a two-phase flow in the post-CHF region under liquid-heated conditions and low wall-superheat. The boiling fluid was water at high pressure, 7.0–15.3 MPa, and mass fluxes in the range of 720–3200 kg/m²s. Experiments were performed in a vertical tube with a 10 mm inside diameter and a 13.1 m heated length. In considering the effects of thermodynamic non-equilibrium and direct drop-wall heat transfer at the low wall-superheats of this investigation (25–100°C), 13 correlations, models and analysis were compared to the data. A review of these formulations is presented including development bases and approaches. The effects of both non-equilibrium and drop-wall heat transfer were evaluated, and recommendations are presented for post-CHF heat transfer predictions at low wall-superheat.     

Characteristics of two-phase one-component flow with slip

All loss-of-coolant-accident analysis codes solve the one-dimensional hydraulic conservation equations for a two-phase compressible fluid. Some codes allow slip between the phases, this slip being specified by a slip model. In this paper the characteristics of these conservation equations with well-known slip models (Jones, Moody, Fauske, Smith and CISE) are evaluated as a function of pressure, quality and mass velocity. Regions in which two of the characteristics are complex are shown on contour maps. The significance of these regions is discussed.     

A model for predicting static instability in two-phase flow systems

An analytical model for predicting the onset of Ledinegg instability in vertical channel under both downflow and upflow conditions has been developed and evaluated. The model divides the flow field into two regions based upon the fluid temperature. The pressure drop is then found by solving an appropriate set of equations for each region. The theoretical results are compared to an existing set of experimental data covering a range of channel diameters and operating conditions. A very good agreement is obtained with the available experimental data from the literature for water systems. A parameter, the ratio between the surface heat flux and the heat flux required to achieve saturation at the channel exit for a given flow rate, is found to be a very accurate indicator of the minimum point velocity in the demand curve.     

Transient equilibrium two-phase flow with quasi-constant slip

A model was created of a transient, one-dimensional, inhomogeneous, two-phase, one-component, equilibrium flow. The idea was used of a quasi steady-state slip in a single element of the rectangular orthogonal mesh of the space in which the numerical solution was sought.Analytical expressions were found for the terms of the matrices before the time and linear coordinate derivatives. The capability of the model in solving transient processes of practical interest was tested. In the tests carried out, the system of 3 partial differential equations was of hyperbolic type.     

CFD studies on the phenomena around counter-current flow limitations of gas/liquid two-phase flow in a model of a PWR hot leg

In order to improve the understanding of counter-current two-phase flow and to validate new physical models, CFD simulations of a 1/3rd scale model of the hot leg of a German Konvoi pressurized water reactor (PWR) with rectangular cross section were performed. Selected counter-current flow limitation (CCFL) experiments conducted at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) were calculated with ANSYS CFX using the multi-fluid Euler–Euler modelling approach. The transient calculations were carried out using a gas/liquid inhomogeneous multiphase flow model coupled with a shear stress transport (SST) turbulence model.In the simulation, the drag law was approached by a newly developed correlation of the drag coefficient (Höhne and Vallée, 2010) in the Algebraic Interfacial Area Density (AIAD) model. The model can distinguish the bubbles, droplets and the free surface using the local liquid phase volume fraction value. A comparison with the high-speed video observations shows a good qualitative agreement. The results indicate also a quantitative agreement between calculations and experimental data for the CCFL characteristics and the water level inside the hot leg channel.     

Steam-generator simulation with non-equilibrium two-phase flow models

The steam-generator model initially developed was a five-equation simulation of the transient behaviour. The present study extends the earlier work by using six field equations to simulate the two-phase flow conditions in the secondary side of the steam generator. Two versions of the six-equation model have been tested. No numerical instabilities were observed. The transient predictions with the two versions were almost identical for the PWR data used in this study.     

Choking flow modeling with mechanical non-equilibrium for two-phase two-component flow

A mechanistic model which considers the mechanical non-equilibrium is described for two-phase choking flow. The choking mass flux is obtained from the momentum equation with the definition of choking. The key parameter for the mechanical non-equilibrium is a slip ratio. The dependent parameters for the slip ratio are identified. In this research, the slip ratio which is defined in the drift flux model is used to identify the impact parameters on the slip ratio. Because the slip ratio in the drift flux model is related to the distribution parameter and drift velocity, the adequate correlations depending on the flow regime are introduced in this study. In this mechanistic modeling approach, the choking mass flow rate is expressed by the function of pressure, quality and slip ratio. The developed model is evaluated by comparing with the air–water experimental data to eliminate the thermal effect. The comparison of predicted choking model for mechanical non-equilibrium with other experimental data in high quality region (up to 80%) is quite reasonable with a small error.     

A self-standing two-fluid CFD model for vertical upward two-phase annular flow

In this paper, a new two-fluid CFD (computational fluid dynamics) model is proposed to simulate the vertical upward two-phase annular flow. This model solves the basic mass and momentum equations for the gas core region flow and the liquid film flow, where the basic governing equations are accounted for by the commercial CFD package Fluent6.3.26^®. The liquid droplet flow and the interfacial inter-phase effects are accounted for by the programmable interface of Fluent, UDF (user defined function). Unlike previous models, the present model includes the effect of liquid roll waves directly determined from the CFD code. It is able to provide more detailed and, the most important, self-standing information for both the gas core flow and the film flow as well as the inner tube wall situations.     

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 modelling and experimental investigation of single-phase and two-phase flow division at a tee-junction

Phase separation in a tee-junction is modelled in the particular case of bubbly-flow. The model is based on a two-dimensional approach and hence, uses local equations. The first step consists in modelling the single-phase flow in the tee-junction. The free streamline theory is used to predict the flow of the continuous phase. The two recirculation zones which are present in this case are predicted by the model. The second step consists in predicting the gas bubble paths as a result of the actions of the single-phase flow. Finally, the trajectories of gas bubbles are used to predict the separation characteristics of the tee-junction. Each step of the modelling procedure has been carefully tested by an in-depth experimental investigation. Excellent quantitative agreement is obtained between experimental results and model predictions. Moreover, the phase separation phenomenon is found to be clearly described by the model.     

Review of two-phase flow instability

Boiling flow in a water-cooled reactor, an evaporator, or an electronic cooling system is susceptible to thermal-hydrodynamic instabilities, which may cause flow oscillations of constant amplitude or diverging amplitude. These oscillations could induce boiling crisis, disturb control systems, or cause mechanical damage. This paper identifies the causes and mechanisms of these instabilities. Based on their mechanisms, various types of instabilities are classified and tabulated. The parametric effects on flow instability, observed experimentally, are systematically presented. Various analytical techniques for predicting the instability threshold are reviewed in terms of their applicability and accuracy.     

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.     

Notes on the implementation of a fully-implicit numerical scheme for a two-phase three-field flow model

The development of a fully-implicit scheme to model the two-phase three-field flow and heat transfer problem is presented here. The model was originally developed to simulate the complex phenomena occurring in proximity of the quench front of a nuclear reactor core during the reflood phase of a postulated LOCA. The fully-implicit method allows relative large time steps to be used even on very fine spatial grids which can not be considered when a semi-implicit scheme is applied to solve the conservation equation. The objective of this paper is to capture as much as possible, the lessons learned during the development and coding of the fully-implicit two-phase three-field model. The implementation of the model is one of the most time consuming and a challenging task. The literature on numerical models generally concentrates on the theoretical aspects of the numerical method but available information on the problems encountered during the implementation of such methods for real applications is scarce. The reason is that many of these methods are tailored to specific applications and sometimes are rather empirical. These techniques are the result of a long and tedious trial and error process from the developer. The article presented here attempts to provide some insights and guidelines for future development of this or similar models.