Development and evaluation of data-driven modeling for bubble size in turbulent air-water bubbly flows using artificial multi-layer neural networks

Abstract In the present study, we consider a new reliable model of the bubble size based on multi-layer artificial neural networks (ANN). A multi-layer ANN is used to establish a function for the bubble size without any assumption on the form. In the training procedure, the proposed ANN is trained using data sets collected from open literature and experiments performed in the present study. An excellent agreement was obtained between the trained ANN and experimental data in the bubble size. Also, sensitivity analyses along with principal component analysis and random forest method provide important physical parameters for the bubble size. Next, in order to rigorously evaluate the prediction capability of the present model, flow simulations were conducted for turbulent bubbly flows, for which experimental data are available. The present validation results show that a regime-adaptive data-driven model for the bubble size achieves successful estimation for both wall and core peaking regimes.

[1]  G. Tryggvason,et al.  Using statistical learning to close two-fluid multiphase flow equations for a simple bubbly system , 2015 .

[2]  Ming Ma,et al.  Using Direct Numerical Simulation and Statistical Learning to Model Bubbly Flows in Vertical Channels , 2017 .

[3]  Donald A. Drew,et al.  A first order relaxation model for the prediction of the local interfacial area density in two-phase flows , 1996 .

[4]  Eckhard Krepper,et al.  Validation of a closure model framework for turbulent bubbly two-phase flow in different flow situations , 2018, Nuclear Engineering and Design.

[5]  Mamoru Ishii,et al.  Interfacial area concentration in steady fully-developed bubbly flow , 2001 .

[6]  G. Bois,et al.  Analysis and modelling of Reynolds stresses in turbulent bubbly up-flows from direct numerical simulations , 2019, Journal of Fluid Mechanics.

[7]  Takashi Hibiki,et al.  Databases of interfacial area concentration in gas–liquid two-phase flow , 2014 .

[8]  Mamoru Ishii,et al.  Two-fluid model and hydrodynamic constitutive relations , 1984 .

[9]  Mamoru Ishii,et al.  One-group interfacial area transport of bubbly flows in vertical round tubes , 2000 .

[10]  Dirk Lucas,et al.  Towards a unified approach for modelling uniform and non‐uniform bubbly flows , 2017 .

[11]  Akio Tomiyama,et al.  Lift force acting on single bubbles in linear shear flows , 2017 .

[12]  A. K. Agrawal,et al.  Shape of liquid drops moving in liquid media , 1966 .

[13]  Hidesada Tamai,et al.  Transverse migration of single bubbles in simple shear flows , 2002 .

[14]  Eckhard Krepper,et al.  Baseline closure model for dispersed bubbly flow: Bubble coalescence and breakup , 2015 .

[15]  N. Dinh,et al.  Classification of machine learning frameworks for data-driven thermal fluid models , 2018, International Journal of Thermal Sciences.

[16]  J. Templeton,et al.  Reynolds averaged turbulence modelling using deep neural networks with embedded invariance , 2016, Journal of Fluid Mechanics.

[17]  Ym Yuk Man Lau,et al.  Development of an image measurement technique for size distribution in dense bubbly flows , 2013 .

[18]  G. Kocamustafaogullari,et al.  Measurement and modeling of average void fraction, bubble size and interfacial area , 1994 .

[19]  Mamoru Ishii,et al.  Local formulation and measurements of interfacial area concentration in two-phase flow , 1986 .

[20]  Takashi Hibiki,et al.  Vertical upward two-phase flow CFD using interfacial area transport equation , 2015 .

[21]  Yang Liu,et al.  Upward vertical two-phase flow local flow regime identification using neural network techniques , 2008 .

[22]  Joshua P. Schlegel,et al.  A correlation for interfacial area concentration in high void fraction flows in large diameter channels , 2015 .

[23]  Nam Dinh,et al.  Data-driven modeling for boiling heat transfer: Using deep neural networks and high-fidelity simulation results , 2018, Applied Thermal Engineering.

[24]  Simon Lo,et al.  The Importance of Correct Modeling of Bubble Size and Condensation in Prediction of Sub-Cooled Boiling Flows , 2012 .

[25]  Jiyuan Tu,et al.  On the numerical study of isothermal vertical bubbly flow using two population balance approaches , 2007 .

[26]  Eckhard Krepper,et al.  Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows , 2007 .

[27]  Byong-Jo Yun,et al.  Evaluation of Bubble Size Models for the Prediction of Bubbly Flow with CFD Code , 2016 .

[28]  Eckhard Krepper,et al.  Unified modeling of bubbly flows in pipes, bubble columns, and airlift columns , 2017 .

[29]  N. Zuber,et al.  Drag coefficient and relative velocity in bubbly, droplet or particulate flows , 1979 .

[30]  J. Joshi,et al.  Advanced PIV/LIF and shadowgraphy system to visualize flow structure in two-phase bubbly flows , 2010 .

[31]  Xinquan Zhou,et al.  Local gas and liquid parameter measurements in air–water two-phase flows , 2013 .

[32]  Mahmoud Meribout,et al.  A NEURAL NETWORK ALGORITHM FOR DENSITY MEASUREMENT OF MULTIPHASE FLOW , 2012 .

[33]  R. V. Mukin,et al.  Modeling of bubble coalescence and break-up in turbulent bubbly flow , 2014 .

[34]  Mamoru Ishii,et al.  Interfacial area concentration of bubbly flow systems , 2002 .

[35]  Min-Ki Kim,et al.  Study of bubble-induced turbulence in upward laminar bubbly pipe flows measured with a two-phase particle image velocimetry , 2016 .

[36]  Lefteri H. Tsoukalas,et al.  Flow regime identification methodology with neural networks and two-phase flow models , 2001 .

[37]  Chul-Hwa Song,et al.  The Effect of Bubble-Induced Turbulence on the Interfacial Area Transport in Gas-Liquid Two-Phase Flow: , 2012 .

[38]  G. Tryggvason,et al.  DNS–Assisted Modeling of Bubbly Flows in Vertical Channels , 2016 .

[39]  Mamoru Ishii,et al.  Local measurement of interfacial area, interfacial velocity and liquid turbulence in two-phase flow , 1998 .

[40]  M. Ishii,et al.  Axial interfacial area transport of vertical bubbly flows , 2001 .

[41]  Simon Lo,et al.  Prediction of a subcooled boiling flow with advanced two-phase flow models , 2012 .

[42]  Kyung Doo Kim,et al.  On the Wall Drag Term in the Averaged Momentum Equation for Dispersed Flows , 2014 .

[43]  Karthik Duraisamy,et al.  Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils , 2016, ArXiv.

[44]  G. Tryggvason,et al.  Using statistical learning to close two-fluid multiphase flow equations for bubbly flows in vertical channels , 2016 .

[45]  Michio Sadatomi,et al.  Momentum and heat transfer in two-phase bubble flow—I. Theory , 1981 .

[46]  Akio Tomiyama,et al.  Multi-fluid simulation of turbulent bubbly pipe flows , 2009 .

[47]  Ik Kyu Park,et al.  Simulations of air–water flow and subcooled boiling flow using the CUPID code , 2013 .