Eigenmodes of Ducted Flows With Radially-Dependent Axial and Swirl Velocity Components

This report characterizes the sets of small disturbances possible in cylindrical and annular ducts with mean flow whose axial and tangential components vary arbitrarily with radius. The linearized equations of motion are presented and discussed, and then exponential forms for the axial, circumferential, and time dependencies of any unsteady disturbances are assumed. The resultant equations form a generalized eigenvalue problem, the solution of which yields the axial wavenumbers and radial mode shapes of the unsteady disturbances. Two numerical discretizations are applied to the system of equations: (1) a spectral collocation technique based on Chebyshev polynomial expansions on the Gauss-Lobatto points, and (2) second and fourth order finite differences on uniform grids. The discretized equations are solved using a standard eigensystem package employing the QR algorithm. The eigenvalues fall into two primary categories: a discrete set (analogous to the acoustic modes found in uniform mean flows) and a continuous band (analogous to convected disturbances in uniform mean flows) where the phase velocities of the disturbances correspond to the local mean flow velocities. Sample mode shapes and eigensystem distributions are presented for both sheared axial and swirling flows. The physics of swirling flows is examined with reference to hydrodynamic stability and completeness of the eigensystem expansions. The effect of assuming exponential dependence in the axial direction is discussed

Transonic flutter calculations using the Euler equations

In transonic flutter problems where shock motion plays an important part, it is believed that accurate predictions of the flutter boundaries will require the use of codes based on the Euler equations. Only Euler codes can obtain the correct shock location and shock strength, and the crucially important shock excursion amplitude and phase lag. The present study is based on the finite volume scheme developed by Jameson and Venkatakrishnan for the 2-D unsteady Euler equations. The equations are solved in integral form on a moving grid. The variable are pressure, density, Cartesian velocity components, and total energy

Active control of wake/blade-row interaction noise through the use of blade surface actuators

A combined analytical/computational approach for controlling of the noise generated by wake/blade-row interaction through the use of anti-sound actuators on the blade surfaces is described. A representative two-dimensional section of a fan stage, composed of an upstream fan rotor and a downstream fan exit guide vane (FEGV), is examined. An existing model for the wakes generated by the rotor is analyzed to provide realistic magnitudes for the vortical excitations imposed at the inlet to the FEGV. The acoustic response of the FEGV is determined at multiples of the blade passing frequency (BPF) by using the linearized unsteady flow analysis, LINFLO. Acoustic field contours are presented at each multiple of BPF illustrating the generated acoustic response disturbances. Anti-sound is then provided by placing oscillating control surfaces, whose lengths and locations are specified arbitrarily, on the blades. An analysis is then conducted to determine the complex amplitudes required for the control surface motions to best reduce the noise. It is demonstrated that if the number of acoustic response modes to be controlled is equal to the number of available independent control surfaces, complete noise cancellation can be achieved. A weighted least squares minimization procedure for the control equations is given for cases in which the number of acoustic modes exceeds the number of available control surfaces. The effectiveness of the control is measured by the magnitude of a propagating acoustic response vector, which is related to the circumferentially averaged sound pressure level (SPL), and is minimized by a standard least-squares minimization procedure

Development of a linearized unsteady Euler analysis for turbomachinery blade rows

A linearized unsteady aerodynamic analysis for axial-flow turbomachinery blading is described in this report. The linearization is based on the Euler equations of fluid motion and is motivated by the need for an efficient aerodynamic analysis that can be used in predicting the aeroelastic and aeroacoustic responses of blade rows. The field equations and surface conditions required for inviscid, nonlinear and linearized, unsteady aerodynamic analyses of three-dimensional flow through a single, blade row operating within a cylindrical duct, are derived. An existing numerical algorithm for determining time-accurate solutions of the nonlinear unsteady flow problem is described, and a numerical model, based upon this nonlinear flow solver, is formulated for the first-harmonic linear unsteady problem. The linearized aerodynamic and numerical models have been implemented into a first-harmonic unsteady flow code, called LINFLUX. At present this code applies only to two-dimensional flows, but an extension to three-dimensions is planned as future work. The three-dimensional aerodynamic and numerical formulations are described in this report. Numerical results for two-dimensional unsteady cascade flows, excited by prescribed blade motions and prescribed aerodynamic disturbances at inlet and exit, are also provided to illustrate the present capabilities of the LINFLUX analysis