Drift-flux Two-phase Flow Model Research Articles

One-dimensional drift-flux model for two-phase flow in NaCl solutions: The role of surface mobility

The presence of dissolved salts in water inhibits bubble coalescence, facilitating the generation of microbubbles, while also maintaining a tangentially mobile air-water surface. In this study, we investigated the variation of bubble size and gas holdup with gas velocity in NaCl solutions using a rectangular bubble column and interpreted the experimental data using the one-dimensional drift-flux model. For the generated bubbles at the size between 0.4 mm and 1 mm, we found that the Moore model assumes mobile air-water surfaces, rather than the Schiller and Naumann model, should be used to describe the bubble terminal velocity. The latter model, which assumes an immobile air-water surface, has been used successfully to predict two-phase flow in surfactant solutions but would overestimate the gas holdup by almost 100 % for NaCl solutions. This finding emphasizes the crucial role of surface mobility in determining gas holdup. Thus, we propose the use of a one-dimensional drift-flux model, incorporating the Moore model to describe bubble terminal velocity, for microbubble systems with a mobile air-water interface.

Global existence of weak solutions to the drift-flux system for general pressure laws

The initial value problem to the multi-dimensional drift-flux model for two-phase flow is investigated in this paper, and the global existence of weak solutions with finite energy is established for general pressure-density functions without the monotonicity assumption.

Vibrational analysis of pipes based on the drift-flux two-phase flow model

Linear and nonlinear free vibrations of supported pipes containing two-phase flow were modeled in different flow regimes by including gravitational force, structural and two-phase damping effects. To model the flow, the drift-flux model was utilized. Discretization of the dynamical equation was performed with the help of the Galerkin scheme. The linear vibrational frequency of the system was determined by solving the eigenvalue problem. Also, a mathematical closed-form expression for the nonlinear vibrational frequency is presented. For the validation purpose, theoretical and experimental data were obtained from literature and compared with the results of this work in various operating conditions. A detailed parametric analysis was also carried out to examine the influence of flow parameters, geometry, and physical properties on the dynamics of the system. It was concluded that by increasing the inner and outer pipe diameters, vibrational frequencies of the system decrease and increase, respectively. It was found that a lower liquid phase density leads to an improvement in the vibrational stability of the system. Besides, it was demonstrated that by increasing the void fraction/mixture velocity in the system, linear and nonlinear vibrational frequencies increase/decrease. Furthermore, a higher initial amplitude caused a larger nonlinear frequency shift. The outcomes of the current analysis can be applied as a frame to evaluate and optimize the performance of structures transporting two-phase flows.

Newton-Krylov method in solving drift-flux two-phase flow problems for both pre-CHF and post-CHF conditions at steady state

This paper presents numerical simulations of two-phase flow heat transfer for both pre-CHF and post-CHF conditions typical in light water nuclear reactors. The conjugate heat transfer problem is modeled with one-dimensional four-equation drift-flux two-phase flow model for coolant flow and two-dimensional heat conduction equation in solid walls/rods. Fully implicit time integration schemes were employed, and the resulted non-linear equations were solved with a Newton-Krylov method. For the drift-flux two-phase flow model, the EPRI drift-flux closure correlation is used to model the relative motion between the two phases. Additional closure correlations were adopted from REALP5-3D to further improve the model accuracy in complex two-phase flow applications. These correlations are applied to determine two-phase flow regime, wall boiling heat and mass transfer, interfacial heat and mass transfer, and two-phase flow frictional pressure drop. Three sets of experiments were used for code validation, including Bartolomei subcooled flow boiling in vertical pipes, FRIGG boiling tests in vertical bundles, and Bennett heated tube tests. RELAP5-3D simulation results were also provided to perform code-to-code benchmark. Overall, numerical results of this work showed good agreements with both experimental data and RELAP5-3D simulation results. Discrepancy between them were also identified in post-CHF region, which suggests necessary further improvement. This work represents the first successful application of Newton-Krylov method in solving four-equation drift-flux two-phase flow problems with a full realistic boiling curve.

On the Riemann Problem Simulation for the Drift-Flux Equations of Two-Phase Flows

This work presents computational simulations and analytical techniques for solving the drift-flux two-phase flow model. The model equations are formulated to describe the exact solution of the Riemann problem. The solution is constructed by solving the conservation of mass for each phase and the mixture conservation momentum equation of the two phases under isothermal conditions. Particular attention is given to address the expressions for jump relationships and the Riemann invariants. The performance of the developed Riemann solver is assessed with respect to different test cases selected from the literature. Comparisons with Godunov methods of centred-type are provided to demonstrate the use of the proposed exact and computational framework. Excellent agreement is observed between analytical results and numerical predictions.

A Robust and accurate Riemann solver for a compressible two-phase flow model

In this paper we analyze the Riemann problem for the widely used drift-flux two-phase flow model. This analysis introduces the complete information that is attained in the representation of solutions to the Riemann problem. It turns out that the Riemann waves have rarefactions, a contact discontinuity and shocks. Within this respect, an exact Riemann solver is developed to accurately resolve and represent the complete wave structure of the gas-liquid two-phase flows. To verify the solver, a series of test problems selected from the literature are presented including validation against independent numerical simulations where the solution of the Riemann problem is fully numerical. In this framework the governing equations are discretized by finite volume techniques facilitating the application Godunov methods of centred-type. It is shown that both analytical and numerical results demonstrate the broad applicability and robustness of the new exact Riemann solver.

Justification of the drift-flux model for two-phase flow in a circular pipe

A flow of a gas-liquid dispersed mixture in a circular pipe with a variable inclination to the horizon, as applied to oil and gas flows in wells, is considered. Within the framework of a multi- fluid approach, the equations of an asymptotic drift-flux model, which contains an algebraic relation between the phase velocities and one momentum equation for the volume-averaged velocity of the mixture, are derived. It is shown that the drift-flux model in this formulation strictly follows from the balance laws under assumption of inertialess velocity slip of the phases in case of validity of one of the following conditions: (i) the dispersed-phase volume fraction is small; (ii) the phase velocity slip may be neglected; or (iii) the flow regime is inertialess and the acceleration of the mixture can be neglected. A numerical algorithm based on the SIMPLE method is implemented for solving the obtained equations of the drift-flux model. The possibility of modeling the gravitational segregation and the pressure buildup in a shut-in well and transient slug flows is demonstrated.

Study on secondary side flow of steam generator with coupled heat transfer from primary to secondary side

Thermohydraulics characteristics in the secondary side of AP1000 steam generator (SG) are simulated based on the porous media models. The drift flux two-phase flow model coupled with a simplified flow boiling model is utilized. The heat transfer from primary side fluid to secondary side fluid is calculated three-dimensionally during iterations. The resistances caused by downcomer, tube bundle, support plates and primary separators are considered. Three-dimensional distributions of velocity, temperature, pressure, enthalpy, density, void fraction and flow vapor quality are obtained from the calculation by using the CFD code ANSYS FLUENT. Flow-induced vibration (FIV) damage is analyzed based on the cross flow velocity over the U-bend region of the outmost U-tube. The most severe FIV damages occur at the angles of −0.544 rad on the cold side and 0.353 rad on the hot side with maximum cross flow energies of 1145.2 J/m3 and 658.9 J/m3, respectively. Fouling is expected to deposit at the bottom of tube bundle since the velocity there is close to zero. The flow vapor qualities of mixture flowing into separators vary from each other significantly, with the maximum and minimum flow vapor quality in separators of 0.659 and 0.073, which is a severe challenge to the capacity design of separators.

One-dimensional drift-flux model for two-phase flow in pool rod bundle systems

A one-dimensional drift-flux model was developed and benchmarked with existing models in the present study. Different from existing empirical correlations, this newly developed 1-D drift-flux model started from the variations of two-phase flow distribution parameter C 0 for non-dimensional superficial gas velocity 〈 j g + 〉 from low to high, which represents the variation of phase distribution patterns. Due to a combination of small-scale sub-channel effect and large-scale casing effect in a rod bundle, the Hibiki–Ishii’s drift velocity V gj + was introduced to describe the relative motion between two phases. A clear boundary of distribution parameter, C 0, can be found when the non-dimensional superficial gas velocity 〈 j g + 〉 is closed to 0.5. A linearly increasing trend and an exponentially decreasing trend of C 0 were found in the lower and higher gas sides divided by this boundary, respectively. Through the present model, one dimensional area-averaged gas velocity and void fraction can be determined for rod bundles in pool conditions. The prediction results were compared with several existing models and experimental data. The present model shows a good agreement with the existing experimental data and can be applied to both boiling and adiabatic air–water two-phase flows. In order to explain the peak values of C 0 in low superficial gas velocity conditions, several possible superficial velocity and void fraction profiles were examined by considering the recirculation flow/void distributions.

The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model

We construct a Roe-type numerical scheme for approximating the solutions of a drift- flux two-phase flow model. The model incorporates a set of highly complex closure laws, and the fluxes are generally not algebraic functions of the conserved variables. Hence, the classical approach of constructing a Roe solver by means of parameter vectors is unfeasible. Alternative approaches for analytically constructing the Roe solver are discussed, and a formulation of the Roe solver valid for general closure laws is derived. In particular, a fully analytical Roe matrix is obtained for the special case of the Zuber-Findlay law describing bubbly flows. First and second-order accurate versions of the scheme are demonstrated by numerical examples.

Subchannel void-fraction measurements in a 6 × 6 rod bundle using a simple gamma-transmission method

A relatively simple subchannel void-fraction measurement system was developed and applied to a scaled model of a BWR fuel assembly. The measurement system is based upon the gamma-transmission technique and uses a tomographic reconstruction procedure to calculate the void-fractions in the subchannels. Data pre-processing is used to remove positioning errors of the gamma source and detector. Measurements are performed under different operating conditions and radial power profiles. The measurements are compared with the drift-flux two-phase flow model. The void-fraction in the wall and corner subchannels is lower than average. By applying the drift-flux model to each subchannel separately and comparing this calculation with measurements the presence of lateral void-drift should be detectable. However, the data do not show evidence for lateral void-drift. By comparing two chordal void-fractions, one through the fuel rods and one in between the fuel rods, a flow pattern transition could clearly be seen between a void-fraction of 30% and 40%.

Verification of the two-phase stratified-flow model in athlet by separate effect tests

The athlet code which is being developed by the Gesellschaft für Anlagen- und Rcaktorsicherheit (GRS) mbH is intended to cover, by means of a single code, the entire spectrum of loss-of-coolant and transient accidents in pressurized and boiling water reactors. The actual athlet version Mod 1.1-Cycle A has a five-equation two-phase model based on the conservation laws for liquid mass, liquid energy, vapor energy and overall momentum. The relative velocity between liquid and vapor is determined by a full-range drift-flux model for two-phase flow in horizontal and vertical pipes. The verification of this drift-flux model is carried out by both large-scale experiments and single-effect tests. The single-effect test ECTHOR investigates stratified flow during the clearance of a water-filled loop seal by a forced air flow through the loop. ECTHOR is a French test for the consideration of two-phase flow regimes in pipes for the development of the cathare codes. The experiments are dedicated to investigating typical two-phase flow during small break loss of coolant accidents (LOCA) in pressurized water reactors (PWR). As a measure, the remaining water level in the loop is determined as a function of the air flow rate. For the verification, a comparison between athlet and cathare computations, on the one hand, and experiments on the other hand is carried out. The results compare very well to each other. Test runs on different numerical grids show convergence to an asymptotic limit with increasing grid refinement.