Combined Turbine and Cycle Optimization for Organic Rankine Cycle Power Systems—Part A: Turbine Model

Abstract

Axial-flow turbines represent a well-established technology for a wide variety of power generation systems. Compactness, flexibility, reliability and high efficiency have been key factors for the extensive use of axial turbines in conventional power plants and, in the last decades, in organic Rankine cycle power systems. In this two-part paper, an overall cycle model and a model of an axial turbine were combined in order to provide a comprehensive preliminary design of the organic Rankine cycle unit, taking into account both cycle and turbine optimal designs. Part A presents the preliminary turbine design model, the details of the validation and a sensitivity analysis on the main parameters, in order to minimize the number of decision variables in the subsequent turbine design optimization. Part B analyzes the application of the combined turbine and cycle designs on a selected case study, which was performed in order to show the advantages of the adopted methodology. Part A presents a one-dimensional turbine model and the results of the validation using two experimental test cases from literature. The first case is a subsonic turbine operated with air and investigated at the University of Hannover. The second case is a small, supersonic turbine operated with an organic fluid and investigated by Verneau. In the first case, the results of the turbine model are also compared to those obtained using computational fluid dynamics simulations. The results of the validation suggest that the model can predict values of efficiency within ± 1.3%-points, which is in agreement with the reliability of classic turbine loss models such as the Craig and Cox correlations used in the present study. Values similar to computational fluid dynamics simulations at the midspan were obtained in the first case of validation. Discrepancy below 12% was obtained in the estimation of the flow velocities and turbine geometry. The values are considered to be within a reasonable range for a preliminary design tool. The sensitivity analysis on the turbine model suggests that two of twelve decision variables of the model can be disregarded, thus further reducing the computational requirements of the optimization.

One-Dimensional Annular Diffuser Model for Preliminary Turbomachinery Design

“…Macchi and Perdichizzi [3] Axial flow Fixed recovery a Lozza et al [5] Axial flow Fixed recovery a Da Lio et al [6] Axial flow Fixed recovery b Astolfi and Macchi [7] Axial flow Fixed recovery b Da Lio et al [8] Axial flow Fixed recovery b Al Jubori et al [9] Axial flow Not considered Talluri and Lombardi [10] Axial flow Not considered Tournier and El-Genk [11] Axial flow Not considered Meroni et al [12] Axial flow Not considered Meroni et al [13] Axial flow Not considered Meroni et al [14] Axial flow Fixed recovery b Perdichizzi and Lozza [15] Radial inflow Fixed recovery a Uusitalo et al [16] Radial inflow Not considered Rahbar et al [17] Radial inflow Not considered Da Lio et al [18] Radial inflow Not considered Pini et al [19] Radial outflow Fixed recovery a Casati et al [20] Radial outflow Fixed recovery a Bahamonde et al [4] Axial flow Radial inflow Radial outflow Not considered a Fixed recovery of the total kinetic energy. b Fixed recovery of the meridional kinetic energy.…”

“…The model can use arbitrary equations of state and it accounts for effects of area change, heat transfer, and friction. Under these conditions the governing equations of the flow are given by Equations (10)- (13). These equations can be derived considering the mass, momentum, and energy balances for the infinitesimal control volume shown in Figure 3.…”

“…This appendix contains the derivation the governing equations for the one-dimensional flow in an annular channel with area change, heat transfer, and friction using arbitrary equations of state. The final version of the equations derived in this appendix were presented within a box and they correspond to Equations (10)- (13) in the main text.…”

A Comparison of Organic and Steam Rankine Cycle Power Systems for Waste Heat Recovery on Large Ships

“…This characteristic would make ORC units attractive propositions for marine waste heat recovery. In order to evaluate further the feasibility of such turbine solutions, a preliminary design study needs to be done using, for example, preliminary design tools [58].…”

Combined Turbine and Cycle Optimization for Organic Rankine Cycle Power Systems—Part B: Application on a Case Study

“…Part A of this two-part paper has presented the structure and validation of the axial turbine simulation tool, TURAX, which provides the preliminary design of single-stage axial-flow turbines [13]. In addition, a sensitivity analysis has been performed in order to reduce the number of decision variables required for the turbine design optimization.…”