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Numerical simulation of transient power consumption characteristics in an unbaffled stirred tank

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Abstract

Numerical simulations were conducted to investigate transient power consumption characteristics in an unbaffled stirred tank. The transient flow field in the stirred tank was simulated using a shear-stress transport k–ω turbulent model. Meanwhile, the transient power number was analyzed based on the predicted impeller torque. The accuracy and reliability of the simulations were verified by experimental data in the literature. The simulation results show that power number undergoes four stages, i.e., plateau value, sharp falling, slow falling and stable stages, after impeller is suddenly started up in quiescent fluid. The curve of transient power number versus dimensionless time is hardly affected by the impeller start-up speed. When impeller speed is accelerated from the same initial speed to higher end speed, the plateau power number becomes higher and the time interval is shorter. With the same speed increment, the plateau power number falls for higher initial speed. Power number falls sharply and then rises gradually to a steady value after impeller speed is decelerated from high to low speed. Time is longer for the power number reaching to steady state when impeller speed is decelerated from same initial speed to lower end speed.

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Abbreviations

A :

Surface area of the blades (m2)

c :

Thickness of blade (m)

C :

Impeller clearance from tank bottom (m)

D :

Impeller diameter (m)

D ω :

Cross-diffusion term (kg m−3 s−2)

r :

Radial location (m)

\(\tilde{G}_{k}\) :

Generation of turbulence kinetic energy (kg m−1 s−3)

G ω :

Generation of ω (kg m−3 s−2)

h :

Impeller height (m)

k :

Turbulent kinetic energy (m2 s−2)

M :

Impeller torque (N m)

N :

Impeller speed (r s−1)

N 0 :

Initial impeller speed (r s−1)

N 1 :

End impeller speed (r s−1)

Npt :

Transient power number

Np∞ :

Plateau power number

Nps :

Steady-state power number

P t :

Transient power consumption (W)

Re:

Reynolds number in the tank

t :

Flow time (s)

t* :

Dimensionless flow time

T :

Tank diameter (m)

u :

Resultant velocity (m s−1)

u i :

Mean velocity component (m s−1)

\(u_{i}^{{\prime }}\) :

Fluctuating velocity of i component (m s−1)

w :

Impeller width (m)

Y k :

Dissipation terms of k (kg m−1 s−3)

Y ω :

Dissipation terms of ω (kg m−3 s−2)

\(\delta_{ij}\) :

Kronecker delta

μ :

Viscosity (Pa s)

μ t :

Turbulent viscosity (Pa s)

ρ :

Density (kg m−3)

ω :

Specific dissipation rate (s−1)

\(\sigma_{k}\) :

Turbulent Prandtl numbers for k

\(\sigma_{\omega }\) :

Turbulent Prandtl numbers for ω

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Acknowledgements

The authors would like to acknowledge the support by Key Scientific Research Project of Sichuan Provincial Education Department (15ZA0107).

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Authors and Affiliations

  1. Key Laboratory of Testing Technology for Manufacturing Process of Ministry of Education, School of Manufacturing Science and Engineering, Southwest University of Science and Technology, Mianyang, 621010, Sichuan, People’s Republic of China

    Liangchao Li, Kefeng Xiang & Beiping Xiang

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  1. Liangchao Li
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  2. Kefeng Xiang
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  3. Beiping Xiang
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Correspondence to Liangchao Li.

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Li, L., Xiang, K. & Xiang, B. Numerical simulation of transient power consumption characteristics in an unbaffled stirred tank. Chem. Pap. 74, 2849–2859 (2020). https://doi.org/10.1007/s11696-020-01115-3

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  • DOI: https://doi.org/10.1007/s11696-020-01115-3

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