Two-Phase Flow Modeling of Solid Dissolution in Liquid for Nutrient Mixing Improvement in Algal Raceway Ponds
Abstract
:1. Introduction
2. Materials and Methods
2.1. Raceway Pond
2.2. Numerical Modeling
2.2.1. Solid–Liquid Modeling
2.2.2. Turbulence Modeling
2.2.3. Mass Transfer Modeling
3. Numerical Simulation and Mesh Generation
4. Results and Discussion
4.1. Experimental Validation
4.1.1. Solid–Liquid Mass Transfer Coefficient
4.1.2. Nutrient Concentrations
4.2. Effect of Pond Aspect Ratio
4.3. Effect of Water Depth
4.4. Effect of Paddle Wheel Rotational Speeds
4.5. Effect of Nutrient Particle Size
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
interfacial area (1/m) | |
aspect ratio (1) | |
initial particle concentration in liquid (mol/m3) | |
dissolved particle concentration in liquid (mol/m3) | |
mass fraction (kg/kg) | |
drag coefficient (1) | |
d | water or pond depth (m) |
solid particle size (m) | |
diffusion coefficient (m2/s) | |
hydraulic diameter (m) | |
dispersion coefficient (m2/s) | |
Froude number (1) | |
gravity vector (m/s2) | |
pond height (m) | |
turbulent kinetic energy (m2/s2) | |
solid–liquid mass transfer coefficient (m/s) | |
L | pond length (m) |
mass transfer rate (kg/(m3∙s)) | |
molecular weight (kg/mol) | |
density number (1) | |
number of particles per volume (1/m3) | |
pressure (Pa) | |
Reynolds number (1) | |
Schmidt number (1) | |
velocity vector (m/s) | |
slip velocity vector (m/s) | |
liquid velocity (m/s) | |
W | water width (m) |
gradient operator | |
Greek Symbols | |
density (kg/m3) | |
turbulent energy dissipation rate (m2/s3) | |
dynamic viscosity (Pa·s) | |
turbulent or eddy viscosity (Pa·s) | |
angular velocity (rad/s) | |
Prandtl number for kinetic energy (1) | |
turbulent particle Schmidt number (1) | |
Prandtl number for dissipation rate (1) | |
volume fraction or holdup (m3/m3) | |
Subscripts | |
continuous phase | |
dispersed phase | |
liquid phase | |
particle | |
solid phase |
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Nutrient | Density (kg/m3) | Particle Size (µm) | Molar Mass (g/mol) |
---|---|---|---|
KNO3 | 2110 | 100 | 101.1 |
Na2HPO4 | 1700 | 100 | 141.96 |
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Ali, H.; Zhang, D.; Wagner, J.L.; Park, C.W. Two-Phase Flow Modeling of Solid Dissolution in Liquid for Nutrient Mixing Improvement in Algal Raceway Ponds. Energies 2018, 11, 899. https://doi.org/10.3390/en11040899
Ali H, Zhang D, Wagner JL, Park CW. Two-Phase Flow Modeling of Solid Dissolution in Liquid for Nutrient Mixing Improvement in Algal Raceway Ponds. Energies. 2018; 11(4):899. https://doi.org/10.3390/en11040899
Chicago/Turabian StyleAli, Haider, Dongda Zhang, Jonathan L. Wagner, and Cheol Woo Park. 2018. "Two-Phase Flow Modeling of Solid Dissolution in Liquid for Nutrient Mixing Improvement in Algal Raceway Ponds" Energies 11, no. 4: 899. https://doi.org/10.3390/en11040899