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Licensed Unlicensed Requires Authentication Published by De Gruyter January 11, 2017

Genetic Programming based Drag Model with Improved Prediction Accuracy for Fluidization Systems

  • R. R. Sonolikar , M. P. Patil , R. B. Mankar , S. S. Tambe and B. D. Kulkarni EMAIL logo


The drag coefficient plays a vital role in the modeling of gas-solid flows. Its knowledge is essential for understanding the momentum exchange between the gas and solid phases of a fluidization system, and correctly predicting the related hydrodynamics. There exists a number of models for predicting the magnitude of the drag coefficient. However, their major limitation is that they predict widely differing drag coefficient values over same parameter ranges. The parameter ranges over which models possess a good drag prediction accuracy are also not specified explicitly. Accordingly, the present investigation employs Geldart’s group B particles fluidization data from various studies covering wide ranges of Re and εs to propose a new unified drag coefficient model. A novel artificial intelligence based formalism namely genetic programming (GP) has been used to obtain this model. It is developed using the pressure drop approach, and its performance has been assessed rigorously for predicting the bed height, pressure drop, and solid volume fraction at different magnitudes of Reynolds number, by simulating a 3D bubbling fluidized bed. The new drag model has been found to possess better prediction accuracy and applicability over a much wider range of Re and εs than a number of existing models. Owing to the superior performance of the new drag model, it has a potential to gainfully replace the existing drag models in predicting the hydrodynamic behavior of fluidized beds.



drag coefficient


particle mean diameter (m)


radial distribution coefficient


unity matrix


2nd invariant of the deviatoric stress tensor (s−2)


gas phase pressure drop (N/m2)


pressure drop due to solids (N/m2)


Reynolds number


strain rate tensor (N/m2)


velocity of phase k (m/s)


fluctuating velocity (m/s)

Greek notation


gas/solid momentum exchange (kg/m3s)


gas volume fraction


solid volume fraction


coefficient used in eq. (6) of Table S.1.


granular temperature (m2/s2)


solid viscosity


collisional viscosity (Pa s)


kinetic viscosity (Pa s)


gas viscocity (Pa s)


viscosity of phase k (Pa s)


bulk viscosity (Pa s)


gas density (kg/m3)


gas stress strain tensor (Pa)


solid stress strain tensor (Pa)


viscous stress tensor (N/m2)


transfer rate of kinetic energy (kg/s3 m)


SST thankfully acknowledges partial support for this study by Council of Scientific and Industrial Research (CSIR), Government of India, New Delhi, under TAPCOAL Network Project.


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Supplemental Material

The online version of this article (DOI: 10.1515/ijcre-2016-0210) offers supplementary material, available to authorized users.

Published Online: 2017-01-11
Published in Print: 2017-04-01

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