Equations (1), (2), (4), (5), (6), (7), (8) and (9) are discretized using finite difference ap­proximations. These equations, together with equations (3) and (10) form the basis of the numerical solution procedure using standard Visual Basic 6.0 code. The performance of the solar tower power plant is evaluated by maximizing the power output by determining the optimum mass flow rate through the system.

3 Results

The maximum power output of the reference plant for the 21st day of selected months are shown in figure 2. The output varies considerably during the day with the peak output de­livered approximately an hour after solar noon. Due to the energy storage capability of the ground, some power is also produced at night. There are significant differences in the output during the summer and winter months. Figure 3 illustrates the temperature distributions in the ground at various times of the day on 21 June and 21 December.

Results show that the reference plant produces 298GWh/a, as is evident from figure 4. Kroger and Buys (2001) also present simulation results for the same reference plant specified in the appendix of this paper. Their model gives an annual plant power output of 341 GWh/a. The model by Kroger and Buys (2001) predicts a higher plant power output compared to this paper due to the following reasons: Kroger and Buys (2001) employ both a developing and fully developed flow region in the collector, the temperature drop across the turbine is not taken into account and most notably a different approach is used to maximize the plant power output.

The plant power output can be increased by altering the shape and inlet height of the collector roof, as shown in figure 4. For the reference plant, a maximum power output is reached with b = 1 and H2 = 3.1 m. The annual plant output is dramatically increased by enlarging the collector diameter or tower height, as indicated by figure 5. An optimal collector inlet height for each collector diameter is shown.

4 Conclusion

The performance of a solar tower power plant is evaluated. Comparative results to earlier studies are found and similar trends established. Numerical simulation results indicate that

the plant power output varies considerably during a typical day and seasonal changes in output are significant. Peak plant output is achieved shortly after midday, while the ground’s energy storage capacity facilitates power generation at night. It is shown that the output of a plant can be increased by optimizing the collector roof shape and inlet height. The power produced by the plant can also generally be increased by increasing the collector diameter or tower height.

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5 Nomenclature

A	Area [m2]	m	Mass flow rate [kg/s]
b	Exponent	n	Refractive index or number
C	Coefficient	P	Pitch [m] or Power [W]
cp	Specific heat capacity [J/kg. K]	P	Pressure [N/m2]
d	Diameter [m]	Pr	Prandtl number
Fr	Froude number	q	Heat flux [W/m2]
f	Friction factor	r	Radius [m]
g	Gravitational acceleration	Re	Reynolds number

References

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A Appendix

For the purpose of comparison, a reference solar tower power plant and a typical operating environment is defined.

The solar radiation values and ambient air temperatures for the reference plant site are given in Table 1 and Table 2 respectively. These meteorological conditions apply to Sishen, South Africa, with latitude 27.67° South and longitude 23.00° East.

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