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Energy Systems Design Accounting for Dynamic Performance implemented by combining basic ThermoPower modules, see Fig. 5.5: 1D flow models for the gas side (top) and fluid side (bottom of the figure), and the 1D thermal model for the tube bundle (middle). The exchange of thermal power is modeled with so-called 1D thermal ports (in orange in the figure); the counter-current model establishes the topological correspondence between the control volumes on the tube walls, and the control volumes on the gas flow model. Figure 5.5: Modelica object diagram of the once-through heat exchanger model The tube metal wall is modeled by a 1D dynamic heat balance equation, discretized by finite volumes. The flow models contain one-dimensional dynamic mass and energy balance equations, discretized by the finite volume method, assuming a uniform pressure distribution; the relatively small friction losses are lumped in an external component model. Here, the pressure drops in off- design conditions are estimated assuming a quadratic dependency from the volumetric flow, with the design point value set from the results of the detailed design step described in §5.4.1. Since the focus of the dynamic analysis is to evaluate the plant performance during critic tran- sients, the models for the convective heat transfer are simplified in comparison to the ones adopted for the heat exchangers design (see §5.4.1). Due to their relatively small contributions, the thermal resistance in the radial direction and thermal diffusion in the axial direction are thus neglected in the dynamic models. The heat transfer coefficient between the gas and the outer pipe surface is much lower than the one between the inner pipe surface and the ORC working fluid flow. Therefore, the overall heat transfer is essentially dependent on the flue gas side only, and the working fluid temperature is always close to the inner surface temperature of the pipe. The heat transfer coefficient at the interface between the flue gas and the metal wall, in off- design conditions, is evaluated with the relation presented in Ref. [31], i.e. m ̇ n m ̇ d e s where ǫ is the heat transfer coefficient, m ̇ the mass flow rate, and the exponent n takes the value 0.6. The thermal interaction between the wall and the working fluid is described by specifying a sufficiently high constant heat transfer coefficient, so that the fluid temperature is close to the wall temperature, and the overall result is dominated by the gas side heat transfer. The model of the ORC turbine is the same as that employed in the design procedure (see Equations (5.4)). In this case, the throat passage area Ath is a fixed parameter obtained from the ǫ = ǫdes , (5.5) 131PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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