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40 Components design 3-1-4 Pressure drop The analysis of the pressure drop is done independently for straight and wavy channels, as shown in the next sections. Straight channels There are four types of losses contributing to the overall pressure drop in the regenerators, friction losses, acceleration losses, local losses and gravitational losses [40]. It is considered that the heat exchanger is horizontal, therefore the gravitational losses can be neglected. Local losses are produced by the contraction and expansion of the working fluid when it enters and leaves the channels. Dostal [16] calculates these losses with local loss coefficients, v2 ∆PLC = CLCρ 2 , (3-18) where v is the velocity of the fluid at the extremes of the channels, and CLC stands for the loss coefficient, which has a value of 0.5 and 1.0 for the channels entrance and exit respectively. Acceleration losses are produced by the change of density in the heat exchanger, 21 1 ∆PAC=G ρ −ρ , (3-19) LE where G is the fluid mass flux, and ρE and ρL are the densities of the fluid entering and leaving the channel respectively. Acceleration losses are negligible compared with the other losses and they are not considered in this work. This assumption is checked in Section 3-1-6. The friction losses are calculated with the Darcy-Weisbach equation, L ρv2 ∆PFR=FDRDHD 2, (3-20) where L is the length of the section. The Darcy friction factor FDR is dependent on the Reynolds number and therefore it is different for each flow regime. For laminar flows with Re < 2000 the friction factor is calculated with the Hagen-Poiseuille law, FDR = 64 . (3-21) Re The departure Reynolds number is the limit for the laminar flow (Re0 = 2000). It is in- dependent from the pipe relative roughness with values smaller than 0.007. Otherwise, the departure Reynolds number has to be calculated [62], 0.0065 Re0 = 754e φ , (3-22) where φ is the relative roughness. The transition region is limited between Re0 and Re = 4000. The friction factor in this region is calculated by means of a linear interpolation between these boundaries. The Blasius law is considered for smooth tubes (φ ≤ 5 · 10−6) and turbulent regimes (Re ≥ 4000), J.S. Bahamonde Noriega FDR = 0.3164Re−0.25. (3-23) Master of Science ThesisPDF Image | Design method for s-CO2 gas turbine power plants
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