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Derivations of Two-Phase Flow Modeling Equations
Published in Clement Kleinstreuer, Theory and Applications, 2017
The primary challenge of utilizing the two-fluid model involves determining the proper form of these constitutive relationships. The most straightforward method would be to average the local instantaneous solution. However, if we knew the instantaneous solution we would not need to solve the averaged equations. Thus this method is used to approximate the constitutive relationships by using known solutions to simpler problems and then extrapolating the results to fit more complicated problems. This method, however, has very serious shortcomings; as the problems of interest diverge from the simple base cases, the validity of the constitutive relations diminishes significantly. Another possible approach would be to base the constitutive relations on empirical data. To obtain the necessary data, experiments would need to be performed to measure the quantities of interest in terms of known values (i.e., the averaged variables). The problems with this approach are similar to those of the previous method with an additional cost factor attached. The constitutive relations are valid only over the range in which the experiments are performed, i.e., the method is not very predictive. A third approach would be to use a combination of the first two methods to produce a predictive model. The averaged equations are used as a guide in determining the proper form of the constitutive relationships. Experimental data are then used to determine the values of constants and functions. This method provides the best all around approach for determining the constitutive relationships.
Heat Transfer, Thermal Hydraulic, and Safety Analysis
Published in Kenneth D. Kok, Nuclear Engineering Handbook, 2016
There are three commonly used two-phase flow models: the homogeneous flow model, separated flow model, and two fluid model. The thermal nonequilibrium allows one or both of the phases to have temperatures other than the saturation temperature and unequal velocities. Separated flow allows not only potential higher gas/vapor velocity but also the possibility of countercurrent flows. The homogeneous flow model does not allow countercurrent flows.
Numerical Simulation of Subcooled Flow Boiling in a Vertical Annulus Channel Under Near Atmospheric Pressure Conditions
Published in Nuclear Science and Engineering, 2023
Sachin Tom, P. Mangarjuna Rao, B. Venkatraman, S. Raghupathy
The CFD simulations of the near-atmospheric pressure flow boiling of water in an annulus channel were carried out by developing the two-fluid model along with the Rensselaer Polytechnic Institute (RPI) wall boiling model for WHFP. The two-fluid model treats liquid and vapor phases separately through two sets of governing equations. The transport of mass, momentum, and energy between the two phases across the interface is described by interfacial constitutive correlations. The flow turbulence is considered using the realizable k- model with standard wall function and mixture-based turbulence treatment. The volume fraction of each phase represents the portion of the flow domain occupied by the corresponding phase and its velocity and temperature field, but all phases share a common pressure field.
Development of three-dimensional simulation method for two-phase flow in square-pitch tube bundle in secondary side of steam generators based on porous drift-flux model
Published in Journal of Nuclear Science and Technology, 2023
Yoshiteru Komuro, Atsushi Kodama, Naotaka Uchimichi, Yoshiyuki Kondo, Tomonori Mineno, Kengo Shimamura, Takashi Hibiki
The two-fluid model solves six conservation equations in total, containing three conservation equations for the gas phase (mass conservation, momentum conservation, and energy conservation) and three for the liquid phase [5,6]. Since it solves gas and liquid separately, the two-fluid model has the ability to reproduce the separation phenomenon of gas and liquid, the formation of liquid pools, and liquid downflows. It takes longer to calculate and has a higher possibility for numerical divergence than the slip model. Since the two-fluid model solves conservative equations for gas and liquid separately, constitutive equations for mass exchange, momentum exchange, and energy exchange between gas and liquid phases. Some constitutive equations, such as interfacial area concentration equations used to calculate momentum exchange, are difficult to validate with temperature and pressure measurement data. The validity explanation of the applied model is insufficient.
Uncertainty Quantification for Multiphase Computational Fluid Dynamics Closure Relations with a Physics-Informed Bayesian Approach
Published in Nuclear Technology, 2023
Yang Liu, Nam Dinh, Xiaodong Sun, Rui Hu
The two-fluid model provides an alternative approach for two-phase flow modeling as a trade-off between computational efficiency and accuracy.9 Adopting the Eulerian-Eulerian approach, the two-fluid model describes the motion of each phase separately and assumes the two phases interact through several mechanisms, such as interfacial shear, phase change, and bubble coalescence/breakup. Compared to the interface tracking methods, the two-fluid model can have a coarser mesh setup as it avoids resolving the interface while it can still capture the local flow features at the desired resolution. As a result, the two-fluid model within the computational fluid dynamics (CFD) framework, i.e., Multiphase Computational Fluid Dynamics (MCFD), is considered a promising tool for two-phase flow modeling in complex engineering systems, such as LWRs.