Computation of Acoustic Waves through Sliding-zone Interfaces Using an Euler/navier-stokes Code

The effect of a patched sliding-zone interface on the transmission of acoustic waves is examined for twoand throe-dimensional model problems. A simple but general interpolation scheme at the patched boundary passes acoustic waves without distortion, provided that a sufficiently small time step is taken. A guideline is provided for the maximum permissible time step or zone speed that gives an acceptable error introduced by the sliding-zone interface. Introduction The prediction and control of ducted fan noise are important elements of the NASA Advanced Subsonic Technology Noise Reduction Program. Current methods of prediction rely extensively on field measurements and analytical scaling techniques. As computers continue to become more powerful, Euler and NavierStokes computer codes for ducted-fan noise prediction have become increasingly affordable. Recent advances in algorithms 1'2,3 that can enhance the efficiency of time-accurate Euler and Navier-Stokes computations also make difficult computations, such as three-dimensional (3D) rotor-stator interactions, better suited for inclusion in future engine design cycles. Previous work by Rai 4 and Gundy-Burlet et al. 5 demonstrated the feasibility of using Navier-Stokes computations for time-accurate rotor-stator interactions. Gundy-Burlet et ai. utilized a combination of overlapping and patched grids; the motion of the rotor relative to the stator was accomplished by "sliding" the rotor grid system past the stator grid system and utilizing a non-conservative linear interpolation to transfer information between the two grid systems. Hall and Delaney 6 employed a similar patched sliding-zone interface strategy to compute ducted prop-fan flows. Chen and Chakravarthy 7 utilized patched sliding-zone interfaces to perform rotor-stator computations. They used a simple piecewise-constant projection of flow variables between grid zone_, with an area-weighting strategy. Janus and Whitfield ° utilized localized grid distortion to pass information between zones that move relative to one another in a prop-fan simulation. Rather than erapioy interpolation, grid points near the zone interface were distorted, then "clicked" to new positions when appropriate. In refs. 4-8, the focus of the computations was the prediction of global aerodynamic characteristics. Rangwalla and RaV compared the numerically calculated tonal acoustics with theoretical values for a twodimensional (2D) rotor-stator interaction. Emphasis was placed on the effects of boundary conditions and boundary extent; however, the effect of the patched slidingzone interface on the accuracy of simulating the passage of acoustic waves was not explored. Because accurate prediction of acoustic waves is essential to any noise-prediction analysis, the effect of the sliding-zone interface on the passage of such waves must be addressed. In the present paper, the effect of a patched sliding-zone interface similar to that employed in refs. 5-7 is examined for several 2D problems, as well as for the passage of typical rotor-stator interaction modes through a 3D duct with a rotating zone. The effects of time step and speed of the moving zone are examined; an engineering rule of thumb for maximum permissible time step or zone speed is developed. Governine E0uations The compressible thin-layer Navier-Stokes equations, written in an inertial reference frame in generalized coordinates, are