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Parabolic Trough Solar System Piping Model Final Report NREL Contract No. AAA-2-32432-01 wall thicknesses such that pressure at the outlet of the hot header is equal to the minimum value set by the user. 8. Unit thermal losses through the pipe insulation are calculated as follows: [8] where k is the thermal conductivity of the insulation, ro is the outside radius of the insulation, and ri is the inside radius of the insulation. The thermal conductivity is evaluated at the average of the inside and the ambient temperatures. The conductivity values are derived from a curve fit of the data on the worksheet labeled “Insulation k vs T”. For the purposes of the model, the thermal resistances of both the inside and the outside convection coefficients are assumed to small compared to the conduction resistance, and, for simplicity, are ignored. Annual Losses Development 1. The annual pumping energy for each segment of pipe is assumed to follow a “cube root mean cubed” function; i.e., the pressure loss is proportional to the square of the velocity, and the pumping power is proportional to the flow rate times the pressure loss. The equations are as follows: ⎡(2)(π)(k, J )(1m)(T , oC -T , oC)⎤ inside ambient ⎥ ⎢ ln() ⎥ Heatloss,J/sec-m=⎢ sec-m-o C ⎢ ri ⎥ ro ⎣⎦ Average flow fraction = and Annual collector fie∑ld operating time, hours 3 (Powertoworking fluid,MWt) 31 Annual collector field operating time,hours Design power to working fluid, MWt [9] m )(3600 sec ) Annual pumpenergydemand,kWhe= (Annual collector field operating time, hours)(Design flow rate, kg/sec)(Average head loss, m)(g c , (1000 J )(3600 sec )(0.75 annual pump efficiency) kW − sec hr [10] where Average head loss, m = (Design head loss, m)(Average flow fraction) The hourly values for the power to the working fluid, shown on the worksheet labeled “HourOutput”, were taken from an Trough Excelergy output file and a weather file for Barstow, California. The annual collector field operating time is 3,436 hours. sec2 hr - 11 - September 15, 2002PDF Image | Parabolic Trough Solar System Piping Model
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