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the detailed pipe model of CYCLES III. Because of the thermal inertia of the pipesβ steel, an approximation of the volume of steel is made for each header based on the ASME required thickness of an equivalent pipe. The ASME minimum required thickness for a circular pipe is given by π‘ β₯ ππ· Eqn. 2-1 2 π + ππ¦ where t is the pipeβs thickness, P is the internal pressure, S is the maximum allowable stress intensity for the material, y is a safety factor equal to 0.4, and D is the outside diameter of the pipe [ASME, 2007]. In CYCLES III, the subroutine HEADERS calculates the header dimensions for TSCYCO by determining approximate: Heat transfer areas, Volumes of steel, and Internal pipe volumes for each of the twelve paths. Then each path is recreated as a single pipe by increasing the length of the pipe and adjusting dimensions to preserve the three quantities listed above. The length is increased until the pressure drop of the header matches that calculated in CYCLES III for the path. Pressure drops are calculated as βπ = π2 ππ£2 π·πΏ + π2 ππ£2 Eqn. 2-2 where Ο is the fluid density, v is the velocity, L is the header length, D is the header diameter, k is a form loss coefficient, and the friction factor, f, is determined from the Blasius correlation for low Reynolds numbers and the McAdams correlation for higher Reynolds numbers [Todreas and Kazimi 1993]. π = 0.316π πβ0.25 , π΅πππ ππ’π ππππππππππ: π π < 30,000 Eqn. 2-3 0.184π πβ0.20 , πππ΄ππππ ππππππππ‘πππ: π π β₯ 30,000 For every pipe in CYCLES III, the form loss factor k was assumed to be 1.50. This comes from a contribution of 1.0 for fluid expansion and 0.5 for fluid contraction at the pipe outlets and inlets, respectively. The dimensions and pressure drops are presented as output in headers.txt. CYCLES III and TSCYCO showed good agreement in the header calculations, producing pressure drops that matched by + 5 % at TSCYCOβs steady state [Trinh, 2009]. 33PDF Image | Supercritical Carbon Dioxide Cycle Analysis
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