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Energies 2020, 13, 5846 8 of 23 where m ̇ WF 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 on the pump design, and ηpmp depends on the volumetric losses, and it can be either introduced as an experimental map (as in the present paper) or calculated by means of a dedicated model, such as the one developed by the authors in previous work [51]. 2. Component #2 is the pipe-template that models the pipe connection of the power plant. In order to reproduce the real hydraulic behavior of the plant in terms of permeability, the real pipe layout is reproduced. To do this, a huge number of pipe elements are involved to reproduce the pipe connections, and each pipe bland and diameter variation is taken into account as well as the material and the surface roughness. For these elements, 1D analysis characterizes the thermo-fluid-dynamic behavior of the working fluid inside the plant, by discretizing the pipes into sub-volumes and by solving balance equations inside each sub-domain in terms of mass conservation (Equation (2)), momentum conservation (Equation (3)), and energy conservation (Equation (4)). These equations are written in 1D, assuming a uniform value for all the quantities in the cross-sectional area of each duct. The fluid-dynamic model is solved through a preliminary linear discretisation of the ducts. Thus, the whole system is subdivided into multiple sub-volumes in contact with each other enclosing a portion of the working fluid. The scalar physical quantities such as pressure, temperature, density, and internal energy are assumed constant within each volume, while the vectorial quantities such as fluid speed and mass flow rate are evaluated on each interface. An implicit method is employed for the integration of the differential equations in order to obtain a simultaneous solution for all the sub-volumes at a certain time step. In this method, the primary variables are the mass flow rate, pressure, and the total enthalpy [52]. dm = m. (2) dt . dpA+m.u−4Cρu|u|dxA−K1pu|u|A dm=dρuA= f2D p2 (3) dt dt dx dρhV =m.h+Vdp−δAs(Tfluid−Twall) (4) dt dt The model allows a physical representation of the ORC based-power plant and the reproduction of its hydraulic behavior, by assessing the effect on the plant permeability of each component and functional connections. As a matter of fact, the permeability α (Equation (5)) can be defined as the ratio of the mass flow rate and pump pressure rise: m. α= WF (5) ∆p 3. Component #3, which is the evaporator, is modeled according a master-slave hierarchy, with the cold side of the evaporator (working fluid side) mastering and the exhaust side acting as the slave. The division in the master and slave section is only a mathematical abstraction, according to which one flow passes through the master and the other passes through the slave. However, the master and the slave together represent the whole behavior of the evaporator accounting for the geometry of the real machine, which eventually allows a proper assessment of both the thermal inertia of the metallic masses and the pressure drops inside.PDF Image | Design of ORC Plant for Low-Grade Waste Heat Recovery
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