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Chapter 5 The basic design procedure of heat exchangers requires determining the surface area by evalu- ating, through an iterative procedure, the overall heat transfer coefficient Uout defined as D log Dout out Din Dout 1 Dout 1 1 1 1 = + + + + , (5.1) Uout hout hout,f 2λtubes Din hin Din hin,f where h is the convective heat transfer coefficient, and D is the tube diameter. λtubes is the thermal conductivity of the tubes material, while “f” refers to the fouling factor. Regarding the once-through boiler, due to the high thermal resistance of the exhaust gases flowing outside the tubes, finned tubes are selected in order to enhance hout. This is modelled by replacing the heat transfer and the fouling coefficients outside the tubes in Eq. (5.1) with a term involving the fins area and their effectiveness. Since the heat transfer occurs in both the single- and the two-phase region, specific equations must be adopted. In case of subcooled liquid and superheated vapor, the heat transfer coefficient inside the tubes is evaluated with the correlations proposed by Gnielinski [17]. The pressure drops related to single-phase flow are estimated using the method described in Ref. [16]. The heat transfer coefficient in the two-phase region is evaluated by discretizing the tubes into finite segments (typically 50) and thus applying the method proposed by Shah [18]. The gas-side heat transfer coefficient is evaluated through the approach proposed in Ref. [19], and the correlation derived therein for the air-side Nusselt number in a finned-tubes heat exchanger reads Nu = 0.22 Re0.6 Pr1/3 (A/Atubes)−0.15 , (5.2) where A is total heat transfer area and Atubes is the outside tubes surface area including the fins. The recuperator is considered to be of the shell-and-tube type, and modelled accordingly, by following Ref. [16]. The tubes are equipped with external fins, in order to enhance the heat transfer coefficient on the shell side, where the fluid is in the superheated vapour state. The corresponding Nusselt number is evaluated as Nu = 0.134 Re0.681 Pr1/3 ((pfin − tfin)/lfin)0.2 (pfin/tfin)0.1134 , (5.3) where pfin, tfin, and lfin are the fin pitch, thickness, and length, respectively. The pressure drops on both sides for the single-phase regions within the tubes are estimated according to Ref. [16]. The total pressure drops occurring in the two-phase flow are estimated by dividing them into three contributions: the static one, vanishing for the proposed configuration (horizontal tubes), the kinematic one, and the one due to viscous friction. The last two terms are evaluated according to the methods proposed in Refs. [20, 21]. For the pressure drops outside the finned tubes the correlation presented in Ref. [22] is adopted. The equation is valid for banks of tubes in cross flow configura- tion, with plain transverse fins, and it can be used for both staggered and in-line arrangement. SUPERSONIC TURBINE The modeled expander is a turbine, which is usually the choice for ORC plants of the considered power capacity. These are usually one- or two-stage axial machines, leading to large pressure ratios across each stage; as a consequence, the flow is usually supersonic at the outlet of the first stator. The expander is therefore modeled as an equivalent choked de Laval nozzle, whose throat flow passage area is the sum of the throat areas of the nozzles constituting the first stator row. Isoentropic expansion is assumed from the inlet section, where total conditions (i.e. total pres- sure PT,6 and total temperature TT,6) are assumed to be known by virtue of the thermodynamic state calculation, to the throat, where sonic conditions are attained, i.e., the flow speed equals the speed 128PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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