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Parabolic Trough Solar System Piping Model Final Report NREL Contract No. AAA-2-32432-01 Optimization Process The procedures for calculating the pipe diameters, wall thicknesses, and insulation thicknesses for each header section are outlined below. The only constraint on the design is the fluid pressure at the exit from the hot header must be equal to a minimum value set by the user. This feature is principally used with a synthetic oil heat transport fluid to ensure the fluid pressure always remains above the vapor pressure. Hydraulic and Thermal Development 1. Basic pipe dimension data, such as nominal diameter, wall thickness, and unit weight, for commercial pipe sizes between 2.5 and 48 inches are shown in the worksheet labeled “PipeData”. 2. Allowable pipe stresses as a function of temperature are shown in the worksheet labeled “SvsT”. For fluid temperatures below 399 °C, the data are applicable for ASTM A106, Grade B, seamless carbon steel pipe. For fluid temperatures between 400 °C and 510 °C, the data are applicable for ASTM A335, Grade P91, low alloy steel. 3. For a given nominal pipe diameter, the required wall thickness is calculated using the familiar equation: (Pressure,bar −1)(Outsidediameter,mm)(100,000 Pa ) Wall thickness,mm = bar (2)(Allowable stress,MPa)(1,000,000 Pa ) + (0.4)(Pressure,bar − 1)(100,000 Pa ) MPa bar [3] The allowable stress is a function of the pipe temperature, and is calculated through a curve fit of the data in “SvsT”. 4. The actual wall thickness is calculated from the minimum wall thickness through the Excel function ActualWall(Dia, MinWall), where ‘Dia’ is the nominal pipe diameter in inches, and ‘MinWall’ is the calculated wall thickness from above. ActualWall is, in essence, a lookup table, which searches for the wall thickness that is the greater of the following: the first commercial pipe wall thickness greater than ‘MinWall’, or a minimum wall thickness of ‘STD’. 5. Friction losses through the header sections, the heat collection elements, and the crossover piping, per meter of length, are calculated using the standard Darcy-Weisbach equation: is calculated using the FricFactor(Rough, Reynold) function in Excel, where ‘Rough’ is ⎡(Velocity, m )2 ⎤ h ,m=(f)⎡ 1m ⎤⎢ sec ⎥ f ⎢⎣Pipeinsidediameter,m⎥⎦⎢ (2)(g , m ) ⎥ ⎢c2⎥ ⎣ sec⎦ where f is the friction factor, and gc is the acceleration due to gravity. The friction factor [4] - 9 - September 15, 2002PDF Image | Parabolic Trough Solar System Piping Model
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