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3-2 Dry cooler 57 properties of the fluid and the mentioned inputs. The friction pressure loss associated with the Darcy-Weisbach friction factor, equation (3-20), reads, LGR ρv2 ∆PFR=FDR D 2, where LGR is the length correspondent to one group of tubes joined by the passes, LGR = LTUBENPASS. (3-87) The velocity of the fluid in the pipe, v, is a function of the mass flow in one pipe, the internal section area and the density, v = fH . (3-88) Aρ The tube mass flow fH is a function of the total mass flow, the number tubes and the number of passes, fH = fTOTNPASS . (3-89) NTUBE Combining the last three expressions it is possible to obtain the number of tubes as a function of the number of passes and tube length, f N L N F ̄ NTUBE = TOT PASS TUBE PASS DR . (3-90) A 2∆PLS ρ ̄ Recall that the pressure loss ∆PFR is caused by friction effects. It is calculated with the total pressure loss and the local losses at the inlet and outlet of the tubes, ∆PFR = ∆PCO − ∆PLC, (3-91) where ∆PLC corresponds to the contraction and expansion losses calculated with expression (3-18). The total pressure drop in the cooler, ∆PCO, is obtained from the thermodynamic analysis and the procedure explained in Section 3-1-5. The bar over the density in equation (3-90) indicates that it is an average property, obtained with the inlet and outlet pressures and temperatures given by the thermodynamic analysis. The friction factor, F ̄DR, is calculated with a different expression, F ̄DR = 1.25(FHE + FHL), (3-92) where FHE and FHL are the Darcy friction coefficients at the inlet and outlet of the pipes, which can be calculated with the procedure for the straight channels in the regenerators model of Section (3-1-4). Notice that equation (3-90) is an implicit expression and it requires an iterative procedure to be solved since the number of tubes is necessary to calculate the friction factors in equation (3-92), and the friction factors are needed to obtain NTUBE. Iterative procedure Two additional iteration procedures are required to dimension the cooler according to the operating conditions given by the thermodynamic analysis. The first regards the hot side Master of Science Thesis J.S. Bahamonde NoriegaPDF Image | Design method for s-CO2 gas turbine power plants
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