CFD-based Evaluation of Interfacial Flows

Gas-liquid two-phase flows with interfacial deformations have been studied in various scientific and industrial fields. However, owing to the complexity of interfacial transient behaviors, the full understanding of gas-liquid two-phase flows is extremely difficult. For example, the occurrence condition of gas entrainment (GE) from free surface is not yet clarified even though a number of studies have been conducted by a lot of researchers. Unexpected GE phenomena often cause problems with equipments or troubles in plant operations (e.g. pump failure) and suppression of their occurrences by flow optimization is strongly required from the viewpoints of operation rates and safety. Therefore, the highlevel understanding of interfacial flows is very important and should be achieved appropriately based on mechanistic considerations. In this Chapter, the authors propose two methodologies to evaluate the GE phenomena in fast reactors (FRs) as an example of interfacial flows. One is a CFD-based prediction methodology (Sakai et al., 2008) and the other is a high-precision numerical simulation of interfacial flows. In the CFD-based prediction methodology, a transient numerical simulation is performed on a relatively coarse computational mesh arrangement to evaluate flow patterns in FRs as the first step. Then, a theoretical flow model is applied to the CFD result to specify local vortical flows which may cause the GE phenomena. In this procedure, two GE-related parameters, i.e. the interfacial dent and downward velocity gradient, are utilized as the indicators of the occurrence of the GE phenomena. On the other hand, several numerical algorithms are developed to achieve the high-precision numerical simulation of interfacial flows. In the development, an unstructured mesh scheme is employed because the accurate geometrical modeling of the structural components in a gas-liquid two-phase flow is important to simulate complicated interfacial deformations in the flow. In addition, as an interface-tracking algorithm, a high-precision volume-of-fluid algorithm is newly developed on unstructured meshes. The formulations of momentum and pressure calculations are also discussed and improved to be physically appropriate at gas-liquid interfaces. These two methodologies are applied to the evaluation of the GE phenomena in experiments. As a result, it is confirmed that both methodologies can evaluate the occurrence conditions of the GE phenomena properly.

[1]  J. Burgers.  A mathematical model illustrating the theory of turbulence , 1948 .

[2]  Larry L. Daggett,et al.  Similitude in Free-Surface Vortex Formations , 1974 .

[3]  P. Woodward,et al.  SLIC (Simple Line Interface Calculation) , 1976 .

[4]  S. Zalesak,et al.  Fully Multidimensional Flux-Corrected Transport. , 1978 .

[5]  Novak Zuber.  1.1 Problems in Modeling of Small Break LOCA , 1980 .

[6]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[7]  L YoungsD,et al.  Time-dependent multi-material flow with large fluid distortion. , 1982 .

[8]  P. Moin,et al.  Eddies, streams, and convergence zones in turbulent flows , 1988 .

[9]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[10]  Isamu Maekawa,et al.  Gas entrainment in the IHX vessel of top-entry loop-type LMFBR , 1994 .

[11]  M. Rudman.  INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, VOL. 24, 671–691 (1997) VOLUME-TRACKING METHODS FOR INTERFACIAL FLOW CALCULATIONS , 2022 .

[12]  Koji Okamoto,et al.  Measurement of flow distribution around a bathtub vortex , 1997 .

[13]  W. Rider,et al.  Reconstructing Volume Tracking , 1998 .

[14]  Marcus R. Maier.  Onsets of liquid and gas entrainment during discharge from a stratified air-water region through two horizontal side branches with centerlines falling in an inclined plane , 1998 .

[15]  R. I. Issa,et al.  A Method for Capturing Sharp Fluid Interfaces on Arbitrary Meshes , 1999 .

[16]  Tomoaki Kunugi,et al.  MARS for multiphase calculation , 2000 .

[17]  S. Zaleski,et al.  Analytical relations connecting linear interfaces and volume fractions in rectangular grids , 2000 .

[18]  D. Fletcher,et al.  A New Volume of Fluid Advection Algorithm , 2000 .

[19]  M. Renardy,et al.  PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method , 2002 .

[20]  Sung-Eun Kim,et al.  A Multi-Dimensional Linear Reconstruction Scheme for Arbitrary Unstructured Mesh , 2003 .

[21]  B Lautrup,et al.  Anatomy of a bathtub vortex. , 2003, Physical review letters.

[22]  E. Puckett,et al.  Second-Order Accurate Volume-of-Fluid Algorithms for Tracking Material Interfaces , 2013 .

[23]  S. Cummins,et al.  Estimating curvature from volume fractions , 2005 .

[24]  Xiaofeng Yang,et al.  Analytic relations for reconstructing piecewise linear interfaces in triangular and tetrahedral grids , 2006, J. Comput. Phys..

[25]  Hideaki Monji,et al.  Proposal of Design Criteria for Gas Entrainment from Vortex Dimples Based on a Computational Fluid Dynamics Method , 2008 .

[26]  H. Kamide,et al.  Experimental Study on Gas Entrainment at Free Surface in Reactor Vessel of a Compact Sodium-Cooled Fast Reactor , 2008 .

[27]  Kei Ito,et al.  Appropriate Formulations for Velocity and Pressure Calculations at Gas-liquid Interface with Collocated Variable Arrangement , 2009 .

[28]  Takumi KAWAMURA,et al.  Formulations and Validations of a High-Precision Volume-of-Fluid Algorithm on Nonorthogonal Meshes for Numerical Simulations of Gas Entrainment Phenomena , 2009 .

[29]  H. Ohshima,et al.  Improvement of Gas Entrainment Prediction Method—Introduction of Surface Tension Effect— , 2010 .