Numerical techniques for non-equilibrium condensing flows are presented. Conservation equations for homogeneous gas-liquid two-phase compressible flows are solved by using a finite volume method based on an approximate Riemann solver. The phase change consists of the homogeneous nucleation and growth of existing droplets. Nucleation is computed with the classical Volmer-Frenkel model, corrected for the influence of the droplet temperature being higher than the steam temperature due to latent heat release. For droplet growth, two types of heat transfer model between droplets and the surrounding steam are used: a free molecular flow model and a semi-empirical two-layer model which is deemed to be valid over a wide range of Knudsen number. The computed pressure distribution and Sauter mean droplet diameters in a convergent-divergent (Laval) nozzle are compared with experimental data. Both droplet growth models capture qualitatively the pressure increases due to sudden heat release by the non-equilibrium condensation. However the agreement between computed and experimental pressure distributions is better for the two-layer model. The droplet diameter calculated by this model also agrees well with the experimental value, whereas that predicted by the free molecular model is too small. Condensing flows in a steam turbine cascade are calculated at different Mach numbers and inlet superheat conditions and are compared with experiments. Static pressure traverses downstream from the blade and pressure distributions on the blade surface agree well with experimental results in all cases. Once again, droplet diameters computed with the two-layer model give best agreement with the experiments. Droplet sizes are found to vary across the blade pitch due to the significant variation in expansion rate. Flow patterns including oblique shock waves and condensation-induced pressure increases are also presented and are similar to those shown in the experimental Schlieren photographs. Finally, calculations are presented for periodically unsteady condensing flows in a low expansion rate, convergent-divergent (Laval) nozzle. Depending on the inlet stagnation subcooling, two types of self-excited oscillations appear: a symmetric mode at lower inlet subcooling and an asymmetric mode at higher subcooling. Plots of oscillation frequency versus inlet sub-cooling exhibit a hysteresis loop, in accord with observations made by other researchers for moist air flow.

Both inflow and outflow velocities near the blade tip become supersonic when the blade length exceeds a threshold limit. The aerofoil near the tip of such a long blade has four features that demand an original supersonic turbine aerofoil design: supersonic flow in the entire field, high reaction, large stagger angle, and large pitch-to-chord ratio. This paper describes design method development for the supersonic turbine aerofoil. First, the aerofoil shape is defined using a curve with continuity in the gradient of the curvature. Second, six loss generation mechanisms are clarified by turbulent flow analysis. Third, an allowable design space between the pitch-to-chord ratio, the stagger angle and the axial-chord-to-pitch ratio is clarified by formulating three geometrical constraints to accelerate supersonic flow smoothly. When there is no solution in the theoretically allowable design space because of the large pitch-to-chord ratio, methods to reduce shock wave losses are proposed. Increasing the outlet metal angle of the pressure surface by around 10 deg from the theoretical outlet flow angle reduces the loss caused by the trailing shock wave. The physical mechanism for this is as follows: the increased outlet metal angle increases the outlet flow passage area so that the overexpansion is suppressed downstream from the flow passage. Fourth, both a cusped leading edge and an upstream pressure surface which has both an angle corresponding to the inflow angle and near-zero curvature can reduce the loss caused by the leading shock wave and satisfy the unique incidence relation. Finally, the aerodynamic performance of the supersonic turbine cascade and the design method are validated by supersonic cascade wind tunnel tests.

Modern steam turbines need to operate efficiently and safely over a wide range of operating conditions. This paper presents a unique unprecedented set of time-resolved steam flowfield measurements from the exit of the last two stages of a low pressure (LP) steam turbine under various volumetric massflow conditions. The measurements were performed in the steam turbine test facility in Hitachi city in Japan. A newly developed fast response probe equipped with a heated tip to operate in wet steam flows was used. The probe tip is heated through an active control system using a miniature high-power cartridge heater developed in-house. Three different operating points, including two reduced massflow conditions, are compared and a detailed analysis of the unsteady flow structures under various blade loads and wetness mass fractions is presented. The measurements show that at the exit of the second to last stage the flow field is highly three dimensional. The measurements also show that the secondary flow structures at the tip region (shroud leakage and tip passage vortices) are the predominant sources of unsteadiness at 85% span. The high massflow operating condition exhibits the highest level of periodical total pressure fluctuation compared to the reduced massflow conditions at the inlet of the last stage. In contrast at the exit of the last stage, the reduced massflow operating condition exhibits the largest aerodynamic losses near the tip. This is due to the onset of the ventilation process at the exit of the LP steam turbine. This phenomenon results in 3 times larger levels of relative total pressure unsteadiness at 93% span, compared to the high massflow condition. This implies that at low volumetric flow conditions the blades will be subjected to higher dynamic load fluctuations at the tip region.

Four-stage low pressure model steam turbine tests are carried out under the low load conditions of 0% to 20% load. In such low load conditions, the reverse flow is generated from turbine exit. Steady pressure measurements using multi-hole pneumatic probes are made to specify the outer boundary of the reverse flow region. The reverse flow regions are determined from the flow angles measured by the multi-hole pneumatic probes, traversing in the radial direction which rotates 360 deg around the longitudinal axis. The outer boundary of the reverse flow regions varies depending on turbine loads and has good agreement with the results of the numerical analyses. The pressure fluctuations are measured using unsteady pressure transducers installed on both the inner and outer side walls of the outlet stage and on the next-stage stationary blade surfaces to investigate the relation between pressure fluctuation and volumetric flow. It is found that the pressure fluctuations, which are defined by the standard deviation of unsteady pressure, become larger with decreased volumetric flow at the outer side as well as the inner side which is the same as the tendency seen for blade dynamic stress characteristics. The authors have previously reported good agreement between the experimental and numerical results. The unsteady pressure probe as another measurement technique is employed to investigate the spanwise pressure fluctuations at the outlet of the moving blade. The results show that as the load decreases, large pressure fluctuations are observed in the vicinity of the outer side after the stages where the reverse flow is observed. This is the same tendency as the results of wall pressure measurements. The generation of large pressure fluctuations, detected by the two different measurement techniques, might have a relationship with the effects of not only the vortex motion in the reverse flow region but also the overall flow field (including main forward flow) oscillated by the multiple vortex motions in the reverse flow region as seen in both experiments and computations. The large pressure fluctuations in the vicinity of the outer side after the blade lead to the increase of exciting force and vibration stress on moving blades. Detailed aerodynamic investigations of these part-load conditions are needed to analyze a blade excitation for further improvement of reliability and availability of steam turbines. The complicated flow structures at low load conditions in a steam turbine can be understood with the aid of both the steady and unsteady flow measurements and calculations.

Modern steam turbines need to operate efficiently and safely over a wide range of operating conditions. This paper presents a unique unprecedented set of time-resolved steam flowfield measurements from the exit of the last two stages of a low pressure (LP) steam turbine under various volumetric massflow conditions. The measurements were performed in the steam turbine test facility in Hitachi city in Japan. A newly developed fast response probe equipped with a heated tip to operate in wet steam flows was used. The probe tip is heated through an active control system using a miniature high-power cartridge heater developed in-house. Three different operating points (OPs), including two reduced massflow conditions, are compared and a detailed analysis of the unsteady flow structures under various blade loads and wetness mass fractions is presented. The measurements show that at the exit of the second to last stage the flow field is highly three dimensional. The measurements also show that the secondary flow structures at the tip region (shroud leakage and tip passage vortices) are the predominant sources of unsteadiness at 85% span. The high massflow operating condition exhibits the highest level of periodical total pressure fluctuation compared to the reduced massflow conditions at the inlet of the last stage. In contrast at the exit of the last stage, the reduced massflow operating condition exhibits the largest aerodynamic losses near the tip. This is due to the onset of the ventilation process at the exit of the LP steam turbine. This phenomenon results in three times larger levels of relative total pressure unsteadiness at 93% span, compared to the high massflow condition. This implies that at low volumetric flow conditions the blades will be subjected to higher dynamic load fluctuations at the tip region.