Direct numerical simulations of bubbly multiphase flows are used to find closure terms for a simple model of the average flow, using Neural Networks (NNs). The flow considered consists of several nearly spherical bubbles rising in a periodic domain where the initial vertical velocity and the average bubble density are homogeneous in two directions but non-uniform in one of the horizontal directions. After an initial transient motion the average void fraction and vertical velocity become approximately uniform. The NN is trained on a dataset from one simulation and then used to simulate the evolution of other initial conditions. Overall, the resulting model predicts the evolution of the various initial conditions reasonably well.
REFERENCES
1.
A.
Esmaeeli
and G.
Tryggvason
, “A direct numerical simulation study of the buoyant rise of bubbles at O(100) Reynolds number
,” Phys. Fluids
17
, 093303
(2005
).2.
M.
van Sint Annaland
, W.
Dijkhuizen
, N.
Deen
, and J.
Kuipers
, “Numerical simulation of gas bubbles behaviour using a 3D front tracking method
,” AIChE J.
52
, 99
–110
(2006
).3.
J.
Lu
and G.
Tryggvason
, “Dynamics of nearly spherical bubbles in a turbulent channel upflow
,” J. Fluid Mech.
732
, 166
–189
(2013
).4.
F. H.
Harlow
and A. A.
Amsden
, “Numerical calculation of multiphase fluid flow
,” J. Comput. Phys.
17
, 19
–52
(1975
).5.
6.
D. A.
Drew
, “Mathematical modeling of two-phase flow
,” Annu. Rev. Fluid Mech.
15
, 261
–291
(1983
).7.
A.
Prosperetti
and G.
Tryggvason
, Computational Methods for Multiphase Flow
(Cambridge University Press
, 2007
).8.
A. T. E.
Labourasse
, D.
Lacanette
, P.
Lubin
, S.
Vincent
, O.
Lebaigue
, J.-P.
Caltagirone
, and P.
Sagaut
, “Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori tests
,” Int. J. Multiphase Flow
33
, 1
–39
(2007
).9.
A.
Toutant
, E.
Labourasse
, O.
Lebaigue
, and O.
Simonin
, “DNS of the interaction between a deformable buoyant bubble and spatially decaying turbulence: A priori tests for les two-phase flow modelling
,” Comput. Fluids
37
, 877
–886
(2008
).10.
A.
Toutant
, M.
Chandesris
, D.
Jamet
, and O.
Lebaigue
, “Jump conditions for filtered quantities at an under-resolved interface. Part 1: Theoretical developments
,” Int. J. Multiphase Flow
35
, 1100
–1118
(2009
).11.
A.
Toutant
, M.
Chandesris
, D.
Jamet
, and O.
Lebaigue
, “Jump conditions for filtered quantities at an under-resolved interface. Part 2: A priori tests
,” Int. J. Multiphase Flow
35
, 1119
–1129
(2009
).12.
J. E.
Juliá
, Y.
Liu
, S.
Paranjape
, and M.
Ishii
, “Upward vertical two-phase flow local flow regime identification using neural network techniques
,” Nucl. Eng. Des.
238
, 156
–169
(2008
).13.
Y.
Mi
, M.
Ishii
, and L.
Tsoukalas
, “Flow regime identification methodology with neural networks and two-phase flow models
,” Nucl. Eng. Des.
204
, 87
–100
(2001
).14.
H. B.
Mehta
, M. P.
Pujara
, and J.
Banerjee
, “Prediction of two phase flow pattern using artificial neural network
,” Network
5
, 6
(2013
).15.
T.
Xie
, S. M.
Ghiaasiaan
, and S.
Karrila
, “Artificial neural network approach for flow regime classification in gas-liquid-fiber flows based on frequency domain analysis of pressure signals
,” Chem. Eng. Sci.
59
, 2241
–2251
(2004
).16.
N.
Al-Rawahi
, M.
Meribout
, A.
Al-Bimani
, A.
Al-Naamany
, and A.
Meribout
, “A neural network algorithm for density measurement of multiphase flow
,” Multiphase Sci. Technol.
24
, 89
–103
(2012
).17.
I.
Rey-Fabret
, R.
Sankar
, E.
Duret
, E.
Heintze
, and V.
Henriot
, “Neural networks tools for improving tacite hydrodynamic simulation of multiphase flow behavior in pipelines
,” Oil Gas Sci. Technol.
56
, 471
–478
(2001
).18.
W.
Warsito
and L.-S.
Fan
, “Neural network based multi-criterion optimization image reconstruction technique for imaging two- and three-phase flow systems using electrical capacitance tomography
,” Meas. Sci. Technol.
12
, 2198
–2210
(2001
).19.
C. M.
Bishop
and G. D.
James
, “Analysis of multiphase flows using dual-energy gamma densitometry and neural networks
,” Nucl. Instrum. Methods Phys. Res., Sect. A
327
, 580
–593
(1993
).20.
C. M.
Bishop
, Pattern Recognition and Machine Learning
, 1st ed. (Springer
, New York, NY
, 2006
).21.
T.
Rajkumar
and J.
Bardina
, “Training data requirement for a neural network to predict aerodynamic coefficients
,” Proc. SPIE
5102
, 92
(2003
).22.
F.
Giralt
, A.
Arenas
, J.
Ferre-Gine
, R.
Rallo
, and G.
Kopp
, “The simulation and interpretation of free turbulence with a cognitive neural system
,” Phys. Fluids
12
, 1826
–1835
(2000
).23.
F.-J.
Chang
, H.-C.
Yang
, J.-Y.
Lu
, and J.-H.
Hong
, “Neural network modelling for mean velocity and turbulence intensities of steep channel flows
,” Hydrol. Processes
22
, 265
–274
(2008
).24.
C.
Lee
, J.
Kim
, D.
Babcock
, and R.
Goodman
, “Application of neural networks to turbulence control for drag reduction
,” Phys. Fluids
9
, 1740
–1747
(1997
).25.
M.
Milano
and P.
Koumoutsakos
, “Neural network modeling for near wall turbulent flow
,” J. Comput. Phys.
182
, 1
–26
(2002
).26.
F.
Sarghini
, G.
de Felice
, and S.
Santini
, “Neural networks based subgrid scale modeling in large eddy simulations
,” Comput. Fluids
32
, 97
–108
(2003
).27.
A.
Moreau
, O.
Teytaud
, and J.-P.
Bertoglio
, “Optimal estimation for large-eddy simulation of turbulence and application to the analysis of subgrid models
,” Phys. Fluids
18
, 105101
(2006
).28.
I.
Esau
and G.
Rieber
, “On application of artificial neural network methods in large-eddy simulations with unresolved urban surfaces
,” Mod. Appl. Sci.
4
, 3
–11
(2010
).29.
J.
Ghaboussi
, J.
Garrett
, Jr., and X.
Wu
, “Knowledge-based modeling of material behavior with neural networks
,” J. Eng. Mech.
117
, 132
–153
(1991
).30.
J. F.
Unger
and C.
Könke
, “Coupling of scales in a multiscale simulation using neural networks
,” Comput. Struct.
86
, 1994
–2003
(2008
).31.
J. F.
Unger
and C.
Könke
, “Neural networks as material models within a multiscale approach
,” Comput. Struct.
87
, 1177
–1186
(2009
).32.
R.
Hambli
, “Numerical procedure for multiscale bone adaptation prediction based on neural networks and finite element simulation
,” Finite Elem. Anal. Des.
47
(7
), 835
–842
(2011
).33.
R.
Hambli
, “Apparent damage accumulation in cancellous bone using neural networks
,” J. Mech. Behav. Biomed. Mater.
4
, 868
–878
(2011
).34.
C.
Lu
, “Artificial neural network for behavior learning from meso-scale simulations, application to multi-scale multimaterial flows
,” M.S. thesis, The University of Iowa
, 2010
.35.
M.
Kuhn
and K.
Johnson
, Applied Predictive Modeling
(Springer
, 2013
).36.
J.
Lu
and G.
Tryggvason
, “Numerical study of turbulent bubbly downflows in a vertical channel
,” Phys. Fluids
18
, 103302
(2006
).37.
J.
Lu
and G.
Tryggvason
, “Effect of bubble size in turbulent bubbly downflow in a vertical channel
,” Chem. Eng. Sci.
62
, 3008
–3018
(2007
).38.
J.
Lu
and G.
Tryggvason
, “Effect of bubble deformability in turbulent bubbly upflow in a vertical channel
,” Phys. Fluids
20
, 040701
(2008
).39.
G.
Tryggvason
, R.
Scardovelli
, and S.
Zaleski
, Direct Numerical Simulations of Gas-Liquid Multiphase Flow
(Cambridge University Press
, 2011
).40.
L.
Vitkin
, D.
Liberzon
, B.
Grits
, and E.
Kit
, “Study of in situ calibration performance of co-located multi-sensor hot-film and sonic anemometers using a ‘virtual probe’ algorithm
,” Meas. Sci. Technol.
25
, 075801
(2014
).41.
T.
Rajkumar
and J.
Bardina
, “Prediction of aerodynamic coefficients using neural networks for sparse data
,” in FLAIRS Conference
, Florida, USA
, 2002
.42.
T.
Hastie
, R.
Tibshirani
, and J.
Friedman
, The Elements of Statistical Learning: Data Mining, Inference and Prediction
, 2nd ed. (Springer
, 2009
).43.
See supplementary material at http://dx.doi.org/10.1063/1.4930004 for averaging of the equations for three-dimensional flows.
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