Visualizing Probabilistic Multi‐Phase Fluid Simulation Data using a Sampling Approach

Eulerian Method of Moment (MoM) solvers are gaining popularity for multi‐phase CFD simulation involving bubbles or droplets in process engineering. Because the actual positions of bubbles are uncertain, the spatial distribution of bubbles is described by scalar fields of moments, which can be interpreted as probability density functions. Visualizing these simulation results and comparing them to physical experiments is challenging, because neither the shape nor the distribution of bubbles described by the moments lend themselves to visual interpretation.

[1]  J. Dormand,et al.  A family of embedded Runge-Kutta formulae , 1980 .

[2]  Hans-Christian Hege,et al.  Uncertain 2D Vector Field Topology , 2010, Comput. Graph. Forum.

[3]  J. Hintze,et al.  Violin plots : A box plot-density trace synergism , 1998 .

[4]  Min Chen,et al.  Over Two Decades of Integration‐Based, Geometric Flow Visualization , 2010, Comput. Graph. Forum.

[5]  Hank Childs,et al.  VisIt: An End-User Tool for Visualizing and Analyzing Very Large Data , 2011 .

[6]  Robert McGraw,et al.  Description of Aerosol Dynamics by the Quadrature Method of Moments , 1997 .

[7]  G. Farin.  Curves and Surfaces for Cagd: A Practical Guide , 2001 .

[8]  H. Rusche.  Computational fluid dynamics of dispersed two-phase flows at high phase fractions , 2003 .

[9]  Kent E. Wardle,et al.  Hybrid Multiphase CFD Solver for Coupled Dispersed/Segregated Flows in Liquid-Liquid Extraction , 2013 .

[10]  Ben Spencer,et al.  Progressive photon relaxation , 2013, ACM Trans. Graph..

[11]  Manuel Menezes de Oliveira Neto,et al.  Overview and State-of-the-Art of Uncertainty Visualization , 2014, Scientific Visualization.

[12]  H. C. Simpson.  Bubbles, drops and particles , 1980 .

[13]  Rüdiger Westermann,et al.  Importance-Driven Particle Techniques for Flow Visualization , 2008, 2008 IEEE Pacific Visualization Symposium.

[14]  Chandra Kambhamettu,et al.  CollisionExplorer: A Tool for Visualizing Droplet Collisions in a Turbulent Flow , 2011, ISVC.

[15]  Daniele Marchisio,et al.  Solution of population balance equations using the direct quadrature method of moments , 2005 .

[16]  Dongbin Xiu,et al.  INTERACTIVE VISUALIZATION OF PROBABILITY AND CUMULATIVE DENSITY FUNCTIONS. , 2012, International journal for uncertainty quantification.

[17]  Daniel Weiskopf,et al.  Texture-based visualization of uncertainty in flow fields , 2005, VIS 05. IEEE Visualization, 2005..

[18]  Daniele Marchisio,et al.  Simulation of coalescence, break-up and mass transfer in a gas-liquid stirred tank with CQMOM , 2013 .

[19]  M. Braga,et al.  Exploratory Data Analysis , 2018, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[20]  Alex T. Pang,et al.  UFLOW: visualizing uncertainty in fluid flow , 1996, Proceedings of Seventh Annual IEEE Visualization '96.

[21]  Mark W. Hlawitschka,et al.  CFD based extraction column design — Chances and challenges , 2016 .

[22]  Mark W. Hlawitschka,et al.  One-Group Reduced Population Balance Model for CFD Simulation of a Pilot-Plant Extraction Column , 2010 .

[23]  Utkarsh Ayachit,et al.  The ParaView Guide: A Parallel Visualization Application , 2015 .

[24]  Hans-Jörg Bart,et al.  Populationsbilanzmodellierung mit einem Mehrphasen‐CFD‐Code und vergleichende Visualisierung , 2016 .

[25]  Joe Michael Kniss,et al.  Visualizing Summary Statistics and Uncertainty , 2010, Comput. Graph. Forum.

[26]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[27]  Martin E. Weber,et al.  Bubbles in viscous liquids: shapes, wakes and velocities , 1981, Journal of Fluid Mechanics.

[28]  S. Katz,et al.  Some problems in particle technology: A statistical mechanical formulation , 1964 .

[29]  Jesse T. Pikturna,et al.  Quadrature method of moments for population‐balance equations , 2003 .

[30]  Rüdiger Westermann,et al.  Streamline Variability Plots for Characterizing the Uncertainty in Vector Field Ensembles , 2016, IEEE Transactions on Visualization and Computer Graphics.