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4-2 Solar tower power plant 79 It is possible now to calculate the solar ray azimuth angle, γSH = sin(αSH)sin(φ) − sin(θ). (4-45) cos(αSH )cos(φ) The unit vector of the sun ray can be expressed with the elevation and azimuth angles, SHU = (cos(αSH)sin(γSH),−cos(αSH)cos(γSH),−sin(αSH)). (4-46) Considering the reference system in Figure 4-11, the unit vector joining the heliostat and the receiver is Spillage factor −x −y z HRU = x2 +y2 +z2,x2 +y2 +z2,x2 +y2 +z2 . (4-47) The spillage factor is the fraction of the energy sent from a heliostat that actually hits the receiver surface. It is calculated with the following expression for a reasonably well focused heliostat [6], receiver. aHT is a parameter function of the overall area of the heliostat, pHHRC σ ,−a ,a pHLRC σ ,−a ,a 2√2 RC RC RC , (4-48) where LRC corresponds to the height of the receiver and WRC to the width (diameter) of the FSP= 2√2 RC RC RC a2RC √ aHT = 2√2σ , (4-49) where AHT is the area of the heliostat and σRC is the dispersion of the effective sunshape on the receiver plane. For convenience expression (4-48) contains a function called pH, 1 1 −(ξ+a)2 1 −(ξ−a)2 pH(ξ,−a,a)=2 (ξ+a)erf(ξ+a)+√πe −(ξ−a)erf(ξ−a)−√πe +const, (4-50) where erf(x) is the error function. Attenuation factor The attenuation factor is related to the losses produced by atmospheric factors and the distance between the heliostats and the receiver. For a clear day, considered in this study, the attenuation factor is [79] FAT = 0.99326 − 0.1046|HR| + 0.017|HR|2 − 0.002845|HR|3, (4-51) where |HR| corresponds to the scalar distance between the heliostat center and the receiver. Master of Science Thesis J.S. Bahamonde Noriega AHT RCPDF Image | Design method for s-CO2 gas turbine power plants
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