The impact of clearance on mixing time for interface-added substrate
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RESEARCH PAPER
The impact of clearance on mixing time for interface‑added substrate Poorya Mirzavand Borujeni1 · Ehsan Ebrahimpoor2 · Navid Mostoufi2 Received: 12 September 2020 / Accepted: 5 November 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This study was carried out to find the optimum clearance (impeller to bottom distance) for Rushton and pitch-blade turbine impellers in a stirred tank bioreactor for improved substrate mixing time added at interface, taking advantage of computational fluid dynamics. In this regard, the time needed for a thin layer of liquid, resembling substrate-rich or poor part, getting homogenously dispersed within the tank was calculated. The mixing time calculated in this way is called the surface aeration related mixing time (SARMT). SARMT was calculated using two approaches and was compared with each other. For the pitch-blade turbine impeller, a criterion which guarantees accurate mixing time by simulation was not satisfied, so the SARMT profile against clearance was not achieved. For the Rushton impeller, a general descending order of SARMT against impeller–bottom clearance was observed. Keywords Computational fluid dynamics (CFD) · Mixing time · Dissolved carbon dioxide · Surface aeration · RANS model Abbreviations b Baffle width (m) C Impeller–bottom clearance (m) C1ε Constant C2ε Constant C3ε Constant CoV Coefficient of variance D Impeller diameter (m) Dm Molecular diffusivity coefficient (m2 s−1) Dt Turbulent diffusivity (m2 s−1) Gb Turbulence kinetic energy generation by buoyancy Gk Turbulence kinetic energy generation by velocity gradients ⇀ g Gravitational acceleration (m s−2) H Height of liquid (m) k Turbulent kinetic energy (m2 s−2) M Torque (N m) N Impeller rotational speed (s−1) NpM Power number calculated using torque draw of rotating surfaces
* Navid Mostoufi [email protected] 1
Department of Biotechnology, College of Science, University of Tehran, P. O. Box 14155/6455, Tehran, Iran
School of Chemical Engineering, College of Engineering, University of Tehran, P. O. Box 11155/4563, Tehran, Iran
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Np𝜀 Power number calculated using volume integral of energy dissipation rate Nq Pumping number p Pressure (Pa) Q Flow rate through the impeller (m3 s−1) S Scalar variable representing the concentration of a species Sc Schmidt number T Tank diameter (m) t Time (s) TC Impeller–top (interface) clearance (m) Uax Axial velocity (m s−1) Utg Tangential velocity (m s−1) U Impeller tip speed (m s−1) ⇀ tip u Velocity vector (m s−1) Greek letters ε Rate of energy dissipation (m2 s−3) µ Molecular viscosity (m2 s−1) µt Turbulent viscosity (m2 s−1) ρ Density (kg m−3) σk K Prandtl number σε ε Prandtl number τ Shear stress (N m−2)
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Introduction Optimal mixing is of the highest concern in bioprocess engineering, to the point that the success of a bioprocess can be evaluated based on the mixing efficiency [1]. Mixing is one of the key criteria considered in the scaleup o
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