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Numerical Investigation of Solid–Liquid Dissolution for Nutrient Mixing Improvement in a Thin-Layer Cascade System

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Abstract

Maintaining an optimal concentration of nutrients in photobioreactors (PBRs) is a key issue for their optimal design and operation. In this study, a numerical investigation was conducted to quantify the dissolution of KNO3 and Na2HPO4 inside a thin-layer cascade (TLC) reactor and determine its consequential effect on the reactor performance for algal cultivation. A computational fluid dynamics (CFD) model based on Euler–Euler approach was used to investigate nutrient mixing in TLC and evaluate the effect of flow and geometric properties of the reactor. A wide range of pertinent parameters such as channel width, channel depth, mass flow rate and nutrient particle size were considered. Nutrient concentration plots, nutrient mixing in terms of mass transfer coefficient, and solid hold-up in the reactor were established. The nutrient dissolution improved in the reactor with small dimensions operating at high mass flow rates and was inversely related to the nutrient particle size; that is, small particle results in increased nutrient mixing due to the enlarged interfacial area.

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Data Availability

Enquiries about data availability should be directed to the authors.

Abbreviations

\(AR\) :

Aspect ratio

\(D\) :

Diffusion coefficient (m2/s)

\(d\) :

Water depth (m)

\({\varvec{u}}\) :

Velocity vector (m/s)

\(W\) :

Channel width (m)

\(A\) :

Cross sectional area (m2)

\(L\) :

Length (m)

\({D}_{h}\) :

Hydraulic diameter (m)

\(\mathrm{a}\) :

Interfacial area (1/m)

\({c}_{\mathrm{c}}\) :

Dissolved particle concentration in liquid (mol/m3)

\({c}_{a}\) :

Initial particle concentration in liquid (mol/m3)

\({c}_{d}\) :

Mass fraction

\(Fr\) :

Froude number (1)

\(Mv\) :

Density number (1)

\({V}_{l}\) :

Liquid velocity (m/s)

\({d}_{p}\) :

Solid particle diameter (m)

\({D}_{md}\) :

Dispersion coefficient (m2/s)

\(Sc\) :

Schmidt number

g\(,\) :

Gravitational vector (m/s2)

\(Re\) :

Reynolds number

\({k}_{sl}\) :

Solid liquid mass transfer coefficient (m/s)

\(M\) :

Molecular weight (kg/mol)

\({m}_{dc}\) :

Mass transfer rate (kg/(m3 s))

\(p\) :

Pressure (Pa)

\({\mathbf{u}}_{\mathrm{slip}}\) :

Slip velocity vector (m/s)

\(n\) :

Number of particle per volume (1/m3)

\(k\) :

Turbulent kinetic energy (m2/s2)

\(\mu \) :

Dynamic viscosity (Pa s)

\({\mu }_{T}\) :

Turbulent viscosity (Pa s)

\({\sigma }_{k}\) :

Prandtl number for kinetic energy

\({\sigma }_{\varepsilon }\) :

Prandtl number for dissipation rate

\(\nabla \) :

Gradient operator

\(\varphi \) :

Volume fraction/hold-up

\(\rho \) :

Water density (kg/m3)

\(\varepsilon \) :

Turbulent energy dissipation rate (m2/s3)

\(p\) :

Particle

\(s\) :

Solid phase

\(d\) :

Dispersed phase

\(c\) :

Continuous phase

\(l\) :

Liquid phase

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Acknowledgements

This study is supported by the National Research Foundation of Korea and funded by the Korean government (MSIP, Grant Nos. 2020R1A2B5B02002512 and 2020R1A4A1018652).

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  1. School of Mechanical Engineering, Kyungpook National University, 80 Daehakro, Buk-Gu, Daegu, 41566, Korea

    Shehnaz Akhtar, Safi Ahmed Memon & Cheol Woo Park

  2. Department of Mathematics & Sciences, College of Humanities & Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

    Sadia Siddiqa

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Akhtar, S., Memon, S.A., Siddiqa, S. et al. Numerical Investigation of Solid–Liquid Dissolution for Nutrient Mixing Improvement in a Thin-Layer Cascade System. Waste Biomass Valor 15, 771–785 (2024). https://doi.org/10.1007/s12649-023-02180-x

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