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Adaptive neuro-fuzzy prediction of flow pattern and gas hold-up in bubble column reactors

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Abstract

The prediction of fluid dynamics in multiphase bubble column reactors is a subject of major concern to appropriately design and optimize them. This paper employs the combination of computational fluid dynamics (CFD) (i.e., Euler–Euler approach) and adaptive neuro-fuzzy inference system (ANFIS) to propose new a viewpoint for multiphase modeling, including the accuracy of soft computing technique in prediction of a 3D bubble column reactor. Existing experimental, numerical and correlations results in the literature have been used to validate the implementation of the Euler–Euler approach. The results of Euler–Euler approach for a 3D bubble column reactor has been used for input training data which are liquid velocity, turbulent kinetic energy and gas hold-up. The ANFIS results have been also compared with Eulerian results, using root-mean-square error (RMSE) and coefficient of determination and Pearson coefficient. The results show that, flow pattern and gas hold-up are mainly affected by bubble column height, meaning towards sparger region, gas hold-up has a higher value near the ring sparger. According to the results, a greater improvement in estimation has been achieved through the ANFIS. Overall, the results show that ANFIS is a robust method to predict bubble column hydrodynamics parameters (e.g., liquid flow pattern and gas hold-up) as input. In addition, the exactness of the proposed ANFIS model may be boosted by considering more meteorological parameters as input values.

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Abbreviations

\(C_{\text{D}}\) :

Drag force coefficient (dimensionless)

\(C_{\text{TD}}\) :

Turbulent dispersion coefficient (dimensionless)

\(C_{\varepsilon 1}\) :

Model parameter in turbulent dissipation energy equation (dimensionless)

\(C_{\varepsilon 2}\) :

Model parameter in turbulent dissipation energy equation (dimensionless)

\(C_{\mu }\) :

Constant in k–ε model (dimensionless)

\(C_{{\mu ,{\text{BI}}}}\) :

Constant in bubble-induced turbulence model (dimensionless)

\(d_{\text{B}}\) :

Bubble diameter (m)

\(d_{0}\) :

Sparger hole diameter (m)

\(D\) :

Diameter of the column (m)

S d :

Sparger diameter

\(g\) :

Gravitational constant (m/s2)

\(G\) :

Generation term (kg/m s2)

\(H\) :

Height (m)

\(k\) :

Turbulent kinetic energy per unit mass (m2/s2)

\(M_{\text{I}}\) :

Total interfacial force acting between two phases (N/m3)

\(M_{\text{e}}\) :

Drag force (N/m3)

\(P\) :

Pressure (N/m2)

\(r\) :

Radial distance (m)

\(R\) :

Column radius (m)

\({\text{Re}}_{\text{B}}\) :

Reynolds number (\(= d_{\text{B}} V_{\text{S}} /v\)) (dimensionless)

\(V_{\text{G}}\) :

Superficial gas velocity (m/s)

\(V_{\text{T}}\) :

Terminal velocity (m2/s)

\(\varepsilon\) :

Turbulent energy dissipation rate per unit mass (m2/s3)

\(\in\) :

Fractional phase hold-up (dimensionless)

\(\bar{ \in }\) :

Average fractional phase hold-up (dimensionless)

\(\mu\) :

Molecular viscosity (Pa s)

\(\mu_{\text{BI}}\) :

Bubble-induced viscosity (Pa s)

\(\mu_{\text{eff}}\) :

Effective viscosity (Pa s)

\(\rho\) :

Density (kg/m3)

\(\mu_{\text{T}}\) :

Turbulent viscosity (Pa s)

\(\sigma\) :

Surface tension (N/m)

\(\sigma_{\varepsilon }\) :

Prandtl number for turbulent energy dissipation rate (dimensionless)

\(\sigma_{k}\) :

Prandtl number for turbulent kinetic energy (dimensionless)

\(\tau_{k}\) :

Shear stress of phase k (Pa)

\({\text{G}}\) :

Gas phase

\({\text{L}}\) :

Liquid phase

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  1. Faculty of Technical Sciences, University of Prishtina, Kneza Milosa 7, Kosovska Mitrovica, Serbia

    Srdjan Jović

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Jović, S. Adaptive neuro-fuzzy prediction of flow pattern and gas hold-up in bubble column reactors. Engineering with Computers 37, 1723–1734 (2021). https://doi.org/10.1007/s00366-019-00905-y

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