Department of Aeronautics and Astronautics
http://hdl.handle.net/1721.1/7758
Fri, 07 Oct 2016 06:44:04 GMT2016-10-07T06:44:04ZAsymptotic analysis of numerical wave propagation in finite difference equations
http://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 wave-like 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, wave-like 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)
Sat, 01 Jan 1983 00:00:00 GMThttp://hdl.handle.net/1721.1/1047681983-01-01T00:00:00ZA numerical analysis of 3-D inviscid stator/rotor interactions using non-reflecting boundary conditions
http://hdl.handle.net/1721.1/104767
A numerical analysis of 3-D inviscid stator/rotor interactions using non-reflecting boundary conditions
Saxer, André P. (André Pierre)
This dissertation presents a method for the computation of three-dimensional 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 3-D Euler equations which incorporates a second-order accurate numerical smoothing for non-uniform grids and steady-state non-reflecting boundary conditions. Fourier analysis applied to the linearized Euler equations is used to develop novel quasi-3-D non-reflecting 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 1-D formulation. The second contribution consists in the study of three specific flow phenomena occurring in an axial flow turbine.; First, the steady-state 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 non-uniformity 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 time-averaged 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 time-averaged results are extremely close to the steady-state 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 230-239)
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/1721.1/1047671992-01-01T00:00:00ZParametric dependencies of aeroengine flutter for flutter clearance applications
http://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 methodology-a test procedure to ensure flutter-free 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 non-dimensional 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 full-scale 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 worst-cases 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 223-228)
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/1721.1/1047662000-01-01T00:00:00ZEffects of inlet conditions on centrifugal diffuser performance
http://hdl.handle.net/1721.1/104763
Effects of inlet conditions on centrifugal diffuser performance
Deniz, Sabri
This report examines the influence of inlet flow conditions, including Mach number, flow angle, blockage, and axial flow non-uniformity, on the performance and operating range of a straight channel centrifugal compressor diffuser. The research was carried out in a unique facility specifically developed to provide the diffuser with a controlled inlet flow. The tests were carried out for inlet Mach number up to values greater than unity and for a range of inlet flow angles up to the onset of rotating stall. It was found that expressing the overall diffuser pressure recovery coefficient, defined using availability or mass averaged inlet total pressure, as a function of momentum averaged diffuser inlet flow angle yields a relationship which is essentially independent of diffuser inlet flow distortion, blockage, or Mach number. Further, the operating range of the diffuser was limited by the onset of rotating stall at a momentum averaged diffuser inlet flow angle ([alpha]crit = 70.5 ±0.5), which was also independent of the inlet flow field axial distortion and Mach number. The straight channel diffuser was designed to be comparable to a previously tested discrete passage diffuser and the performance of the two was compared; the overall pressure recovery of the former was found to be roughly 10% higher than that of the latter. Both diffuser types, straight channel and discrete passage diffuser showed similar behavior regarding the insensitivity of the performance and operating range to inlet flow axial non-uniformities and Mach number. The report also presents information on recent developments in the area of centrifugal compressor diffusers together with a detailed review of the open literature.
March 1997; Includes bibliographical references (pages 169-190)
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/1721.1/1047631997-01-01T00:00:00Z