Solar Energy pp 95-114 | Cite as

# Mathematical Modelling of Solar Updraft Tower

## Abstract

Solar updraft tower power plant is a way to harness energy from the sun. It is a simple concept which requires low maintenance and utilises land that is already being used for growing plants, and generates power from it. A prototype plant was setup in Manzanares, Spain. Numerical analysis on power generation is performed for a similar plant assuming it is setup in Ropar. By considering losses via convection and radiation through the top surface of the collector, collector efficiency is calculated. Two cases arise here, 1. With 100% collector efficiency and 2. Collector efficiency is obtained after subtracting convection and radiation losses. The influx of solar radiation is highest in June. Hence, the variation of parameters like temperature, velocity, power output, efficiency with time of the day is done by taking averages for the month of June. Next the impact of physical parameters like chimney height, chimney radius and collector radius are studied on 21st June 11:00 to 12:00. How each parameter impacts the output of the plant is studied by creating a mathematical model of the power plant. Methods to improve the power output are discussed.

## Keywords

Solar energy Solar updraft tower Collector Chimney Wind turbine## Nomenclature

*A*Area (m

^{2})*C*Power coefficient for wind turbine,

*C*= 0.45*C*_{p}Specific heat at constant pressure for air (J/kg K),

*C*_{p}= 1007 J/kg K*g*Acceleration due to gravity (m/s

^{2}),*g*= 9.81 m/s^{2}*G*_{sc}Solar constant (W/m

^{2}),*G*_{sc}= 1367 W/m^{2}*h*Convective heat transfer coefficient (W/m

^{2}K)*H*Height (m)

*I*_{o}Hourly incident solar energy on an extra-terrestrial horizontal surface (J/m

^{2})*m*Refractive index

*ṁ*Mass flow rate of air (kg/s)

*n*Day of the year

*p*Pressure (Pa)

*P*Power (kW)

*Q*Heat (W)

*Q*″Hourly average incident heat flux (W/m

^{2})*r*Radius (m)

*R*Characteristic gas constant (J/kg K),

*R*= 287 J/kg K*T*Temperature (°C)

*v*Velocity (m/s)

## Greek symbols

*ε*Emissivity

*η*Efficiency (%)

*ρ*Density (kg/m

^{3})*σ*Stefan-Boltzmann’s constant (W/m

^{2}K^{4}),*σ*= 5.67 × 10^{−8}W/m^{2}K^{4}*τ*Transmissivity

## Subscripts

*chim*Chimney

*coll*Collector

*conv*Convection

*i*Inlet of turbine/chimney

*o*Ambient

*ovr*Overall

*rad*Radiation

*turbine*Turbine

## Notes

### Acknowledgements

The authors (K. V. S. T., K. G. and H. T.) wish to express their gratitude to the School of Mechanical Material and Energy Engineering at Indian Institute of Technology Ropar for their support.

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