Gas Turbine Laboratory
https://hdl.handle.net/1721.1/104381
20210724T22:10:55Z

Asymptotic analysis of numerical wave propagation in finite difference equations
https://hdl.handle.net/1721.1/104768
Asymptotic analysis of numerical wave propagation in finite difference equations
Giles, M. (Michael); Thompkins, William T.
An asymptotic technique is developed for analysing the propagation and dissipation of wavelike solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equation's. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wave packet theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wavelike disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed which gives results which agree with other stability analyses and which can be applied to a wider range of problems.
March 1983; Also issued as: Thesis (M.S.)Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1983; Includes bibliographical references (page 134)
19830101T00:00:00Z

A numerical analysis of 3D inviscid stator/rotor interactions using nonreflecting boundary conditions
https://hdl.handle.net/1721.1/104767
A numerical analysis of 3D inviscid stator/rotor interactions using nonreflecting boundary conditions
Saxer, AndrĂ© P. (AndrĂ© Pierre)
This dissertation presents a method for the computation of threedimensional inviscid, transonic steady and unsteady flows, primarily in axial flow turbines. The work is divided into two major contributions. The first is an algorithm for the solution of the 3D Euler equations which incorporates a secondorder accurate numerical smoothing for nonuniform grids and steadystate nonreflecting boundary conditions. Fourier analysis applied to the linearized Euler equations is used to develop novel quasi3D nonreflecting boundary conditions at the inflow/outflow and at the stator/rotor interface. The accuracy, effectiveness and robustness of the boundary condition formulation is demonstrated through several subsonic and transonic test cases and through comparison with the standard 1D formulation. The second contribution consists in the study of three specific flow phenomena occurring in an axial flow turbine.; First, the steadystate effects of an inlet spanwise stagnation temperature gradient in a transonic stage are analyzed. The mechanism for the migration of the temperature as well as the extent of the nonuniformity are assessed. Then, the secondary flow produced by a combined thermal and vortical inlet distortion on a downstream moving rotor is studied. The extent of the radial mixing for steady and unsteady flow is assessed as a function of the strength of the inlet disturbance. The third case is an analysis of the steady, unsteady and timeaveraged flow fields in a highly loaded industrial transonic turbine stage. In particular, the unsteady shock interaction due to the impact of the stator trailing edge shock wave off the downstream rotor is studied. From the last two cases it is concluded that in many aspects the timeaveraged results are extremely close to the steadystate values, even with strong unsteady shock interaction.; For each case the mechanisms for the creation of the secondary flow and deviations from a steady, uniform inlet conditions flow field are presented and analyzed.
March 1992; Includes bibliographical references (pages 230239)
19920101T00:00:00Z

Parametric dependencies of aeroengine flutter for flutter clearance applications
https://hdl.handle.net/1721.1/104766
Parametric dependencies of aeroengine flutter for flutter clearance applications
Khalak, Asif, 1972
This thesis describes the effects of operational parameters upon aeroengine flutter stability. The study is composed of three parts: theoretical development of relevant parameters, exploration of a computational model, and analysis of fully scaled test data. Results from these studies are used to develop a rational flutter clearance methodologya test procedure to ensure flutterfree operation. It is shown, under conditions relevant to aeroengines, that four nondimensional parameters are necessary and sufficient for flutter stability assessment of a given rotor geometry. We introduce a new parameter, termed the reduced damping, g/p*, which collapses the combined effects of mechanical damping and mass ratio (blade mass to fluid inertia). Furthermore, the introduction of the compressible reduced frequency, K*, makes it possible to uniquely separate the corrected performance map from the nondimensional operating environment (including inlet temperature and pressure).; Simultaneous plots of the performance map of corrected mass flow and corrected speed, (mc,nc), with the (K*, g/p*) map provide a dimensionally complete and fully integrated view of flutter stability, as demonstrated in the context of a historic multimission engine. A parametric, .computational study was conducted using a 2D, linearized unsteady, compressible, potential flow model of a vibrating cascade. This study showed the independent effects of Mach number, inlet flow angle, and reduced frequency upon flutter stability in terms of critical reduced damping, which corroborates the 4D view of flutter stability. Test data from a fullscale transonic fan, spanning the full 4D parameter space, were also analyzed. A novel boundary fitting tool was developed for data processing, which can handle the generic case of sparse, multidimensional, binary data.; The results indicate that the inlet pressure does not alone determine the flight condition effects upon flutter, which necessitates the use of the complete 4D parameter set. Such a complete view of the flutter boundary is constructed, and sensitivities with respect to various parameters are estimated. A rational flutter clearance procedure is proposed. Trends in K* and g/p* allow one to rapidly determine the worstcases for testing a given design. One may also use sensitivities to extend the results of sea level static (SLS) testing, if the worst case is relatively close to the SLS condition.
August 2000; Includes bibliographical references (pages 223228)
20000101T00:00:00Z

Measurements of rotor stalling in a matched and a mismatched multistage compressor
https://hdl.handle.net/1721.1/104764
Measurements of rotor stalling in a matched and a mismatched multistage compressor
Silkowski, Peter D. (Peter Daniel)
This paper presents the results from a set of experiments on stall inception in multistage axial flow compressors. The experiments were tailored to investigate phenomena having a wide range of time and length scales. This range of scales was motivated by two previously observed paths to stall. Parametric changes such as tip clearance, inlet distortion and mismatch were carried out to demonstrate the importance of component coupling in the stall inception process. Evidence is presented for the importance of the local compressor characteristic in determining where and when the initiation of the stall inception process will occur. Although the stall inception process may begin as a localized event, its growth into rotating stall is governed by the environment established by the coupling of the various compression system components. Finally, the tip flow field, specifically the rotor tip leakage jet, is shown to be a key feature in the stall inception process.
April 1995; Includes bibliographical references (page 21)
19950101T00:00:00Z