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Energies 2020, 13, x FOR PEER REVIEW 8 of 24 component of the ORC plant, whose main components and functional connections are shown in Energies 2020, 13, 5846 9 of 23 Figure 5 and modeled according the components listed below. FFigiguurree55..DDiaiaggraramooffththeeORRCC-b-baasseeddppooweerrpplalannttmooddeel.l. In the master–slave approach reported in Figure 6, the HRVG walls are sub-divided into 1. Component #1 represents the gear pump, which is modeled as a single component 60 sub-volumes, and for each time step, the solver evaluates the thermal energy exchanged between characterized by its volumetric capacity and thermodynamic performance, i.e., the the exhaust gases and working fluid P . The model considers heat transfer as the combination of volumetric and adiabatic isentht,reocpic efficiency. The present work is based on the data two contributions, one related to the thermal conduction through the HRVG wall and the other related obtained from an extensive experimental campaign by the authors [8], but in the most to the convective heat exchange between each fluid and the adjacent HRVG wall. The thermal power general case, it can be retrieved from a comprehensive model of the machine, which exchanged P is evaluated according to Equation (6): confitrhm,resc the versatility of the present approach. The pump revolution speed is varied through an inverted mounted on an asynchronous electric motor. Thus, being a volumetric Pth,rec = UAs∆T (6) machine, if the revolution speed, ωpmp, is set, the mass flow rate circulating inside the plant, where: ṁWF,thepumpvolumetricefficiency,ηpmp,andthepumpintakevolume,Vin,pmp,areknown. The pump was modeled as in Equation (1): • A representstheareaofheatexchangedeterminedbythemodelforeachsub-volumeasafunction s of HRVG geometry introduced asa calculation input; = ,, (1) 60 • ∆T is the temperature logarithmic mean difference between each fluid evaluated as a function of where ṁWF depends on the density of the working fluid at the pump intake ρin,pmp, which is set by the heat sink conditions, ωpmp is an operating condition introduced as an input parameter, Vin,pmp depends • U represents a whole convective heat exchange coefficient evaluated at each analysis step and for the HRVG configuration; on the pump design, and ηpmp depends on the volumetric losses, and it can be either introduced as an each sub-volume based on the condition of fluid motion, its thermophysical properties, and the experimental map (as in the present paper) or calculated by means of a dedicated model, such as the roughness of the duct surfaces. The product UAs is evaluated from: one developed by the authors in previous work [5151]. 2. Component #2 is the pipe-template that models the pipe connection of the power plant. In 1 order to reproduce the real hydraulic behavior of the plant in terms of permeability, the real UAs= 1 tw 1 (7) pipe layout is reproduced. To do this, a+huge n+umber of pipe elements are involved to Um Am kw Aw Usl AslPDF Image | Design of ORC Plant for Low-Grade Waste Heat Recovery
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