INVISCID BLADE-TO-BLADE PREDICTION OF A WAKE-GENERATED UNSTEADY FLOW.

A description is presented of a time-marking calculation of the unsteady flow generated by the interaction of upstream wakes with a moving blade row. The inviscid equations of motion are solved using a finite volume technique. Wake dissipation is modeled using an artificial viscosity. Predictions are presented for the rotor mid-span section of an axial turbine. Reasonable agreement is found between the predicted and measured unsteady blade surface static pressures and velocities. These and other results confirm that simple theories can be used to explain the phenomena of rotor-stator wake interactions.

Effect of blade tip geometry on the tip leakage flow in axial turbine cascades

The phenomenon of tip leakage has been studied in two linear cascades of turbine blades. The investigation includes an examination of the performance of the cascades with a variety of tip geometries. The effects of using plain tips, suction side squealers, and pressure side squealers are reported. Traverses of the exit flow field were made in order to determine the overall performance. A method of calculating the tip discharge coefficients for squealer geometries is put forward. In linking the tip discharge coefficient and cascade losses, a procedure for predicting the relative performance of tip geometries is developed. The model is used to examine the results obtained using the different tip treatments and to highlight the important aspects of the loss generation process.

Secondary flows and loss caused by blade row interaction in a turbine stage

A study of the three-dimensional stator-rotor interaction in a turbine stage is presented. Experimental data reveal vortices downstream of the rotor which are stationary in the absolute frame - indicating that they are caused by the stator exit flowfield. Evidence of the rotor hub passage vortices is seen, but additional vortical structures away from the endwalls, which would not be present if the rotor were tested in isolation, are also identified. An unsteady computation of the rotor row is performed using the measured stator exit flowfield as the inlet boundary condition. The strength and location of the vortices at rotor exit are predicted. A formation mechanism is proposed whereby stator wake fluid with steep spanwise gradients of absolute total pressure is responsible for all but one of the rotor exit vortices. This mechanism is then verified computationally using a passive-scalar tracking technique. The predicted loss generation through the rotor row is then presented and a comparison made with a steady calculation where the inlet flow has been mixed out to pitchwise uniformity. The loss produced in the steady simulation, even allowing for the mixing loss at inlet, is 10% less than that produced in the unsteady simulation. This difference highlights the importance of the time-accurate calculation as a tool of the turbomachine designer.

Development of blade profiles for low pressure turbine applications

This paper describes a program of work, largely experimental, which was undertaken with the objective of developing an improved blade profile for the low-pressure turbine in aero-engine applications. Preliminary experiments were conducted using a novel technique. An existing cascade of datum blades was modified to enable the pressure distribution on the suction surface of one of the blades to be altered. Various means, such as shaped inserts, an adjustable flap at the trailing edge, and changing stagger were employed to change the geometry of the passage. These experiments provided boundary layer and lift data for a wide range of suction surface pressure distributions. The data was then used as a guide for the development of new blade profiles. The new blade profiles were then investigated in a low-speed cascade that included a set of moving bars upstream of the cascade of blades to simulate the effect of the incoming wakes from the previous blade row in a multistage turbine environment.

Numerical simulations of unsteady wet steam flows with non-equilibrium condensation in the nozzle and the steam turbine

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. Copyright © 2006 by ASME.

Blade Loading and Its Application in the Mean-Line Design of Low Pressure Turbines

In order to minimize the number of iterations to a turbine design, reasonable choices of the key parameters must be made at the preliminary design stage. The choice of blade loading is of particular concern in the low pressure (LP) turbine of civil aero engines, where the use of high-lift blades is widespread. This paper considers how blade loading should be measured, compares the performance of various loss correlations, and explores the impact of blade lift on performance and lapse rates. To these ends, an analytical design study is presented for a repeating-stage, axial-flow LP turbine. It is demonstrated that the long-established Zweifel lift coefficient (Zweifel, 1945, "The Spacing of Turbomachine Blading, Especially with Large Angular Deflection" Brown Boveri Rev., 32(1), pp. 436-444) is flawed because it does not account for the blade camber. As a result the Zweifel coefficient is only meaningful for a fixed set of flow angles and cannot be used as an absolute measure of blade loading. A lift coefficient based on circulation is instead proposed that accounts for the blade curvature and is independent of the flow angles. Various existing profile and secondary loss correlations are examined for their suitability to preliminary design. A largely qualitative comparison demonstrates that the loss correlations based on Ainley and Mathieson (Ainley and Mathieson, 1957, "A Method of Performance Estimation for Axial-Flow Turbines," ARC Reports and Memoranda No. 2974; Dunham and Came, 1970, "Improvements to the Ainley-Mathieson Method of Turbine Performance Prediction," Trans. ASME: J. Eng. Gas Turbines Power, July, pp. 252-256; Kacker and Okapuu, 1982, "A Mean Line Performance Method for Axial Flow Turbine Efficiency," J. Eng. Power, 104, pp. 111-119). are not realistic, while the profile loss model of Coull and Hodson (Coull and Hodson, 2011, "Predicting the Profile Loss of High-Lift Low Pressure Turbines," J. Turbomach., 134(2), pp. 021002) and the secondary loss model of (Traupel, W, 1977, Thermische Turbomaschinen, Springer-Verlag, Berlin) are arguably the most reasonable. A quantitative comparison with multistage rig data indicates that, together, these methods over-predict lapse rates by around 30%, highlighting the need for improved loss models and a better understanding of the multistage environment. By examining the influence of blade lift across the Smith efficiency chart, the analysis demonstrates that designs with higher flow turning will tend to be less sensitive to increases in blade loading. © 2013 American Society of Mechanical Engineers.