This paper presents the application of an adjoint method to the aerodynamic design optimization of a turbine blade. With the adjoint method, the complete gradient information needed for optimization can be obtained by solving the governing flow equations and their corresponding adjoint equations only once, regardless of the number of design parameters. The formulations including imposition of appropriate boundary conditions for the adjoint equations of the Euler equations for turbomachinery problems are presented. Two design cases are demonstrated for a turbine cascade that involves a high tip flare, characteristic of steam turbine blading in low-pressure turbines. The results demonstrate that the design optimization method is effective and the redesigned blade yields weaker shock and compression waves in the supersonic region of the flow while satisfying the specified constraint. The relative effects of changing blade profile stagger, modifying the blade profile shape, and changing both stagger and profile shape at the same time are examined and compared. Navier-Stokes calculations are performed to confirm the performance at both the design and off-design conditions of the blade designed by the Euler method.
We present a study of three-stream nozzle concepts with potential to reduce takeoff noise of future commercial supersonic aircraft. The concepts were evaluated at realistic cycle conditions in a subscale acoustic facility. Computations solving the Reynolds-Averaged Navier-Stokes equations provided insight into the changes in the flow field that can impact noise generation. The investigation encompassed long-and short-cowl nozzles in coaxial and asymmetric arrangements where the third stream was concentrated in the downward azimuthal direction. In coaxial configurations, addition of the third stream makes a modest impact on the noise emission, with a small benefit at high frequencies in the aft arc. This benefit is more evident in short-cowl nozzles. Asymmetric arrangements involved offsetting the tertiary duct and/or application of an internal wedge-shaped deflector. The asymmetry produces significant noise reduction in the direction of the thickened tertiary flow, and is more effective at cycle conditions with high specific thrust. Reduction of the skewness of the far-field pressure fluctuations suggests suppression of Mach wave radiation by the asymmetric tertiary flow.
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