Evaluation of ANN and ANFIS Methods in Study of the Motion of a Bubble in A Combined Couette-Poiseuille Flow

Document Type : Original Article

Authors

1 Department of Mechanical Engineering, Shahrekord University, Shahrekord, Iran

2 Department of Mechanical Engineering, Bu-Ali Sina University, Hamedan, Iran

Abstract

The equilibrium position of a deformable bubble in a combined Couette-Poiseuille flow is investigated numerically by solving the full Navier-Stokes equations using a finite-difference/front-tracking method. The present approach is examined to predict the migration of a bubble in a combined Couette-Poiseuille flow at finite Reynolds numbers of 5, 10, and 15. The related unsteady incompressible full Navier-Stokes equations are solved using a conventional finite-difference method with a structured staggered grid. The purpose of this study is to evaluate ANN and ANFIS methods in study of the lateral migration of the bubble. Evaluation criteria of accuracy in test set derived from ANFIS demonstrates that estimated values of correlation coefficient (r), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) are 0.97, 0.001, and 0.0014, respectively. The ANN model with RMSE of 0.0007, MAE of 0.0004 and r of 0.99, is better than ANFIS model. It is also demonstrated that the bubble position estimated by the ANN and ANFIS models closely follows the one achieved from front tracking method. 

Keywords


[1]     Taylor, G. I., The Deformation of Emulsions in Definable Fields of Flow, Proceeding of The Royal Society, Vol. A146, 1934, pp. 501–523.
[2]     Segre, G., Silberberg, A., Behavior of Macroscopic Rigid Spheres in Poiseuille Flow Part 2. Experimental Results and Interpretation, Vol. 14, No. 1, 1962, pp. 136-157.
[3]     Karnis, A., Mason, S. G., Particle Motions in Shear Suspension, Part 3. Wall Migration of Fluid Drops, Colloid Interface Science, Vol. 24, 1967, pp. 164-169.
[4]     Halow, J. S., Willis, G. B., Radial Migration of Spherical Particles in Couette System, AICHE Journal, Vol. 16, 1970, pp. 281-286.
[5]     Zhou, H., Pozrikidis, C., The Flow of Suspensions in Channels: Single Files of Drops, Physics of Fluids, Vol. 2, 1993, pp. 311-324.
[6]     Feng, J., Hu, H. H., and Joseph, D. D., Direct Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid, Part2. Couette Flow and Poiseuille Flows, Journal of Fluid Mechanics, Vol. 277, 1994, pp. 271−301.
[7]     Saffman, P. G., The Lift On a Small Sphere in A Slow Shear Flow, Journal of Fluid Mechanics, Vol. 22, 1965, pp. 385-400.
[8]     Li, X., Zhou, H., and Pozrikidis, C., A Numerical Study of the Shearing Motion of Emulsions and Foams, Journal of Fluid Mechanics, Vol. 286, 1995, pp. 374−404.
[9]     Mortazavi, S., Tryggvason, G., A Numerical Study of the Motion of Drop in Poiseuille Flow Part1: Lateral Migration of One Drop, Journal of Fluid Mechanics, Vol. 411, 2000, pp. 325−350.
[10]  Goodarzi, Z., Ahmadi Nadooshan, A., and Bayareh, M., Numerical Investigation of Off-Center Binary Collision of Droplets in A Horizontal Channel, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 40, 2018, pp. 1-10. http://dx.doi.org/10.1007/s40430-018-1075-y
[11]  Armandoost, P., Bayareh, M., and Ahmadi Nadooshan, A., Study of the Motion of a Spheroidal Drop in A Linear Shear Flow, Journal of Mechanical Science and Technology, Vol. 32, 2018, pp. 2059-2067. http://dx.doi.org/10.1007/s12206-018-0415-2
[12]  Bayareh, M., Mortazavi, S., Effect of Density Ratio On the Hydrodynamic Interaction Between Two Drops in Simple Shear Flow, Iranian Journal of Science and Technology, Vol. 35, 2011, pp. 441-452. DOI: 10.22099/ijstm.2011.900
[13]  Bayareh, M., Mortazavi, S., Equilibrium Position of a Buoyant Drop in Couette and Poiseuille Flows at Finite Reynolds Numbers, Journal of Mechanics, Vol. 29, 2013, pp. 53-58. http://dx.doi.org/10.1017/jmech.2012.109
[14]  Bayareh, M., Mortazavi, S., Geometry Effects On the Interaction of Two Equal-Sized Drops in Simple Shear Flow at Finite Reynolds Numbers, 5th International Conference: Computational Methods in Multiphase Flow, WIT Trans. Eng. Sci., Vol. 63, 2009, pp. 379-388.
[15]  Bayareh, M., Mortazavi, S., Migration of a Drop in Simple Shear Flow at Finite Reynolds Numbers: Size and Viscosity Ratio Effects, Proceeding of International Conference on Mechanical, Industriel and Manufacturing Engineering (ICMIME), Cape Town, South Africa, 2010.
[16]  Mohammadi Masiri, S., Bayareh, M., and Ahmadi Nadooshan, A., Pairwise Intercation of Drops in Shear-Thinning Inelastic Fluids, Korea-Australia Rheology Journal, Vol. 31, No. 1, 2019, pp. 25-34. https://doi.org/10.1007/s13367-019-0003-8
[17]  Bayareh, M., Nourbakhsh, A., Study of the Bubble Motion in A Compound Couette-Poiseuille Flow: Effect of The Pressure Gradient, Advances in Modelling and Analysis A, Vol. 55, No. 1, 2018, pp. 11-19. https://doi.org/10.18280/ama_a.550102
[18]  Bayareh, M., Dabiri, S., and Ardekani, A. M., Interaction Between Two Drops Ascending in A Linearly Stratified Fluid, European Journal of Mechanics-B/Fluids, Vol. 60, 2016, pp. 127-136. http://dx.doi.org/10.1016/j.euromechflu.2016.07.002.
[19]  Nayak, P. C., Sudheer, K. P., Rangan, D. M., and Ramasastri, K. S., A Neuro-Fuzzy Computing Technique for Modeling Hydrological Time Series, Journal of Hydrology, Vol. 291, 2004, pp. 52-66.
[20]  Chaves, P., Kojiri, T., Deriving Reservoir Operational Strategies Considering Water Quantity and Quality Objectives by Stochastic Fuzzy Neural Networks, Advances in Water Resources, Vol. 30, 2007, pp. 1329-1341.
[21]  Zoveidavianpoor, M., A Comparative Study of Artificial Neural Network and Adaptive Neurofuzzy Inference System for Prediction of Compressional Wave Velocity, Neural Computing and Applications, Vol. 25, 2014, pp. 1169–1176
[22]  Unverdi, S. O., Tryggvason, G., A Front-Tracking Method for Viscous Incompressible Multi-Fluid Flows, Journal of Computational Physics, Vol. 100, 1992, pp. 25-82
[23]  Unverdi, S. O, Tryggvason, G., Computations of Multi-Fluid Flows, Physics, Vol. D60, 1992, pp. 70-83
[24]  Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S., and Jan, Y. J., A Front-Tracking Method for the Computations of Multiphase Flow, Journal of Computational Physics, Vol. 169, 2001, pp. 708-759
[25]  Adams, J., MUDPACK: Multigrid FORTRAN Software for The Efficient Solution of Linear Elliptic Partial Differential Equations, Applied, Mathematics and Computation, Vol. 34, 1989, pp. 113-146
[26]  Schonberg, J. A., Hinch, E. J., Inertial Migration of a Sphere in Poiseuille Flow, Journal of Fluid Mechanics, Vol. 203, 1989, pp. 517-524
[27]  Yang, B. H., Wang, J., Joseph, D. D., Hu, H. H., Pan, T. W., and Glowinski, R., Migration of a Sphere in Tube Flow, Journal of Fluid Mechanics, Vol. 540, 2005, pp. 109-131
[28]  Asmolov, E. S., The Inertial Lift On a Spherical Particle in A Plane Poiseuille Flow at Large Channel Reynolds Number, Journal of Fluid Mechanics, Vol. 381, 1999, pp. 63-87
[29]  ASCE Task Committee on Application of Artificial Neural Networks in Hydrology. Artificial neural networks in hydrology: I. Preliminary Concepts, Journal of Hydraulic Engineering, Vol. 5, No. 2, 2000, pp. 124–137.
[30]  Govindaraju, R. S., Rao, A. R., Artificial Neural Networks in Hydrology, Kluwer Academic Publishers, Amsterdam, the Netherlands, 2000.
[31]  Nasseh, S., Mohebbi, A., Sarrafi, A., and Taheri, M., Estimation of Pressure Drop in Venturi Scrubbers Based On Annular Two-Phase Flow Model, Artificial Neural Networks and Genetic Algorithm, Chemical Engineering Journal, Vol. 150, 2009, pp. 131–138
[32]  Parthiban, L., Subramanian, R., Intelligent Heart Disease Prediction System using CANFIS and Genetic Algorithm, International Journal of Biological and Medical Sciences, Vol. 3, 2008, pp. 157-160
[33]  Aytek, A., Co-Active Neurofuzzy Inference System for Evapotranspiration Modeling, Soft Computing-A Fusion of Foundations, Methodologies and Applications, Vol. 13, No. 7, 2008, pp. 691-700
[34]  Takagi, T., Sugeno, M., Fuzzy Identification of Systems and Its Applications to Modeling and Control, IEEE Transactions on Systems, Vol. 15, No. 1, 1985, pp. 116–132
[35]  Jalali-Heravi, M., Asadollahi-Baboli, and M., Shahbazikhah, P., QSAR Study of Heparanase Inhibitors Activity Using Artificial Networks and Levenberg-Marquardt Algorithm, European Journal of Medicinal Chemistry, Vol. 43, 2008, pp. 548-556
[36]  Tabari, H., Marofi, S., and Sabziparvar, A. A., Estimation of Daily Pan Evaporation Using Artificial Neural Network and Multivariate Non-Linear Regression, Irrigation Science, Vol. 28, 2010, pp. 399-406
[37]  Nourbakhsh, A., Ghahremani, Z., and Zojaji, M., Entropy Generation Minimization of a MHD Flow over a Rotating Disk using Artificial Neural Network and Artificial Bee Colony, Majlesi Journal of Energy Management, Vol. 3, No. 4, 2014, pp. 29-40
[38]  Piri, J., Mohammadi, K., Shamshirband, S., and Akib, S., Assessing the Suitability of Hybridizing the Cuckoo Optimization Algorithm with ANN and ANFIS Techniques to Predict Daily Evaporation, Environmental Earth Sciences, Vol. 75, No. 3, 2016, pp. 1-13.