Techniques for analyzing rotating rake mode measurements over passive treatment

Abstract

The NASA Glenn Research Center’s rotating rake mode measurement system has been successful in measuring the modal content propagating in hard-wall ducts. This paper proposes an extension of the rotating rake measurement and analysis technique to treated sections by developing basis functions based on wall impedance boundary conditions for flow conditions (i.e. constant duct area and Mach number), where the closed-form analytical solution exists. Analytical equations developed to estimate mode power are incorporated. Using the impedance boundary conditions results in better mode measurement solutions. This method is verified by decomposing and analyzing radial pressure profiles generated numerically by the Eversman propagation code. Several modes, frequencies, and impedances are evaluated. For ducts with soft-walls and mean flow, the radial basis functions must be numerically computed. The linear companion matrix method is used to obtain both the eigenvalues of interest, without the need for an initial guess, and the radial basis functions. The governing equations allow for the mean flow to have a boundary layer at the wall. In addition, a nonlinear least-squares method is used to adjust the wall impedance to best fit the data in an attempt to use the rotating system as an in-duct wall impedance measurement tool. Simulated and measured data are used to show the effects of wall impedance and mean flow on the computed results. Data from an inlet of a low-speed ducted fan with several different impedance conditions on the outer wall were acquired and reduced to determine the best fit to the data. The methodology and analysis documented in this paper were directly inspired by the groundbreaking work of Dr. Edward J Rice.