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ABSTRACT
A numerical investigation is conducted to study the performance of solar wind energy towers. The two-phase flow of air and water droplets in the tower is modeled following an Euler–Lagrange approach with air representing the continuous phase and water droplets the discrete phase. Results demonstrate that energy towers perform best in hot and dry environments. Water injection at the inlet to a tower increases the strength of the downdraft current with the rate of increase diminishing as the flow at exit approaches saturation. At a given water injection rate and tower diameter the downdraft strength increases as the height increases, while it is independent of the diameter at constant height. Energy analysis shows that for towers of low height the cost of electricity is expensive and commercially unfeasible, while it is cheap for towers of heights higher than 100 m.
Nomenclature
| Ad | = | droplet surface area (m2) |
| Bm | = | Spalding mass transfer number |
| BT | = | Spalding heat transfer number |
| cp,d | = | water droplet specific heat (J/kg K) |
| CD | = | drag coefficient |
| dd | = | water droplet diameter (m) |
| D | = | tower diameter (m) |
| Dv | = | diffusivity of water vapor in air (m2/s) |
| E | = | total energy (J/kg) |
| h | = | convection heat transfer coefficient (W/m2 K) |
| H | = | tower height (m) |
| hfg | = | latent heat of evaporation (J/kg) |
| hv | = | vapor enthalpy (J/kg) |
| k | = | turbulence kinetic energy (J/kg) |
| md | = | droplet mass (kg) |
| = | mass flow rate of the gas mixture (kg/s) | |
| Nu | = | Nusselt number |
| p | = | pressure (Pa) |
| Pr | = | Prandtl number |
| Q | = | enhancement in mass flow rate |
| r | = | radial coordinate (m) |
| Red | = | Reynolds number based on the droplet diameter |
| Sm | = | source term in continuity and vapor mass fraction equations |
| Sh | = | source term in energy equation |
| Sx | = | source term in x-momentum equation |
| Sr | = | source term in r-momentum equation |
| Sh | = | Sherwood number |
| Sc | = | Schmidt number |
| t | = | time (s) |
| T | = | temperature (K) |
| Tair | = | air temperature (K) |
| Td | = | droplet temperature (K) |
| Tref | = | reference temperature for enthalpy (K) |
| vd | = | droplet velocity vector |
| vx | = | axial component of velocity (m/s) |
| vr | = | radial component of velocity (m/s) |
| v | = | velocity vector of the continuous phase |
| Vair | = | velocity of moist air (m/s) |
| W | = | humidity ratio (kgvapor/kgdryair) |
| x | = | axial coordinate (m) |
| xd | = | droplet position vector |
| Yv | = | mass fraction of water vapor in the gas phase |
| Greek symbols | = | |
| ε | = | turbulence dissipation rate (J/kg s) |
| μ, μt | = | laminar and turbulent viscosity (kg/m s2) |
| λ | = | effective thermal conductivity (W/m K) |
| ρ | = | air density (kg/m3) |
| ρd | = | droplet density (kg/m3) |
| ϕ | = | relative humidity |
Nomenclature
| Ad | = | droplet surface area (m2) |
| Bm | = | Spalding mass transfer number |
| BT | = | Spalding heat transfer number |
| cp,d | = | water droplet specific heat (J/kg K) |
| CD | = | drag coefficient |
| dd | = | water droplet diameter (m) |
| D | = | tower diameter (m) |
| Dv | = | diffusivity of water vapor in air (m2/s) |
| E | = | total energy (J/kg) |
| h | = | convection heat transfer coefficient (W/m2 K) |
| H | = | tower height (m) |
| hfg | = | latent heat of evaporation (J/kg) |
| hv | = | vapor enthalpy (J/kg) |
| k | = | turbulence kinetic energy (J/kg) |
| md | = | droplet mass (kg) |
| = | mass flow rate of the gas mixture (kg/s) | |
| Nu | = | Nusselt number |
| p | = | pressure (Pa) |
| Pr | = | Prandtl number |
| Q | = | enhancement in mass flow rate |
| r | = | radial coordinate (m) |
| Red | = | Reynolds number based on the droplet diameter |
| Sm | = | source term in continuity and vapor mass fraction equations |
| Sh | = | source term in energy equation |
| Sx | = | source term in x-momentum equation |
| Sr | = | source term in r-momentum equation |
| Sh | = | Sherwood number |
| Sc | = | Schmidt number |
| t | = | time (s) |
| T | = | temperature (K) |
| Tair | = | air temperature (K) |
| Td | = | droplet temperature (K) |
| Tref | = | reference temperature for enthalpy (K) |
| vd | = | droplet velocity vector |
| vx | = | axial component of velocity (m/s) |
| vr | = | radial component of velocity (m/s) |
| v | = | velocity vector of the continuous phase |
| Vair | = | velocity of moist air (m/s) |
| W | = | humidity ratio (kgvapor/kgdryair) |
| x | = | axial coordinate (m) |
| xd | = | droplet position vector |
| Yv | = | mass fraction of water vapor in the gas phase |
| Greek symbols | = | |
| ε | = | turbulence dissipation rate (J/kg s) |
| μ, μt | = | laminar and turbulent viscosity (kg/m s2) |
| λ | = | effective thermal conductivity (W/m K) |
| ρ | = | air density (kg/m3) |
| ρd | = | droplet density (kg/m3) |
| ϕ | = | relative humidity |