An analysis of the friction losses in a centrifugal compressor stage is used to suggest a new form of correction equation for the effect of Reynolds number on efficiency. This equation relates the effect of Reynolds number to the surface roughness, the impeller outlet width ratio and the work input coefficient. Systematic tests on a wide range of compressor stages are used to calibrate the single empirical coefficient in the equation. Despite its simplicity this equation provides more accurate predictions of the Reynolds number effects than existing empirical methods.
A novel approach to calculate the performance map of a centrifugal compressor stage is presented. At the design point four nondimensional parameters (the flow coefficient φ, the work coefficient λ, the tip-speed Mach number M, and the efficiency η) characterize the performance. In the new method the performance of the whole map is also based on these four parameters through physically based algebraic equations which require little prior knowledge of the detailed geometry. The variable empirical coefficients in the parameterized equations can be calibrated to match the performance maps of a wide range of stage types, including turbocharger and process compressor impellers with vaned and vaneless diffusers. The examples provided show that the efficiency and the pressure ratio performance maps of turbochargers with vaneless diffusers can be predicted to within ±2% in this way. More uncertainty is present in the prediction of the surge line, as this is very variable from stage to stage. During the preliminary design the method provides a useful reference performance map based on earlier experience for comparison with objectives at different speeds and flows.
The jet discharged from the nozzle of a Pelton turbine is a key item of such hydropower systems and its precise shape and position are highly relevant to the optimum design of the turbine buckets to match the incoming flow. Experimental investigations, primarily with laser Doppler anemometry, have been used to identify the important fluid dynamic structures of the jet and its free surface. It is shown that weak secondary flows generated by the bends or bifurcations in the distributor of the Pelton turbine system are still present in the jet leaving the injectors. These cause small flow disturbances which affect the shape, orientation, and the topology of the jets and lead to a shift of the jet core from the axis of the nozzle.
Two-phase computational fluid dynamics modelling is used to investigate the magnitude of different contributions to the wet steam losses in a three-stage model low pressure steam turbine. The thermodynamic losses (due to irreversible heat transfer across a finite temperature difference) and the kinematic relaxation losses (due to the frictional drag of the drops) are evaluated directly from the computational fluid dynamics simulation using a concept based on entropy production rates. The braking losses (due to the impact of large drops on the rotor) are investigated by a separate numerical prediction. The simulations show that in the present case, the dominant effect is the thermodynamic loss that accounts for over 90% of the wetness losses and that both the thermodynamic and the kinematic relaxation losses depend on the droplet diameter. The numerical results are brought into context with the well-known Baumann correlation, and a comparison with available measurement data in the literature is given. The ability of the numerical approach to predict the main wetness losses is confirmed, which permits the use of computational fluid dynamics for further studies on wetness loss correlations.
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