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141 sound. In addition, ORC radial turbines present high expansion ratio and Mach number at the stator exit due to the frequently changing specific volume, which results in supersonic flows. This outcome necessitates the use of a real EoS rather than the traditionally adopted Mach relationships for ideal gas. The thermodynamic properties at each station must likewise be checked simultaneously through the turbine stage. According to the authorsβ knowledge, no such methodologies are available in the open literature. Once the basic geometric parameters of the turbine are calculated using the DPC, the geometry is subsequently exported to the off-design code to evaluate the turbine performance at different operating conditions. The outputs of the current code are the characteristic curves or performance maps. These maps can be integrated in any ORC model to investigate the effectiveness of the turbine in the overall cycle performance. A carefully selected nozzle model is used because supersonic expansion is an expected phenomenon in high-pressure ratio turbines. In addition, flow is expected to choke at the throat at high-pressure ratios. Therefore, a special treatment is also considered when choking occurs. The author implies that the proposed methodology is the first methodology that can be used to estimate the performance of radial-inflow turbines integrated in ORC applications. 5.7.1 Description of the Methodology Compared with the DPC, the off-design procedure begins from the volute and ends at the rotor exit. In each station, the continuity equation is used as the control point where convergence must be achieved. A detailed loss model from the open literature is also applied to investigate the real performance of the turbine. Figure β5-14presents the flowchart of the full off-design modelling. At the volute inlet, absolute velocity πΆ1 is considered an initial value. Static enthalpy is subsequently calculated using the First Law of Thermodynamics, as shown in equation(β5-56). The other thermodynamic properties are subsequently calculated using the EoS at π1,π1 . The process is repeated until convergence is achieved, as shown in equation(β5-68).PDF Image | Automotive Radial Turbine Expander Design WHR
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