<p>In order to eliminate or reduce vibration problems inturbomachines without a high increase in the complexity of thevibratory behavior, the adjacent airfoils around the wheel areoften mechanically connected together with lacing wires, tip orpart-span shrouds in a number of identical sectors. Although anaerodynamic stabilizing effect of tying airfoils together ingroups on the whole cascade is indicated by numerical andexperimental studies, for some operating conditions suchsectored vane cascade can still remain unstable.</p><p>The goal of the present work is to investigate thepossibilities of a sectored vane cascade to undergoself-excited vibrations or flutter. The presented method forpredicting the aerodynamic response of a sectored vane cascadeis based on the aerodynamic work influence coefficientrepresentation of freestanding blade cascade. The sectored vaneanalysis assumes that the vibration frequency is the same forall blades in the sectored vane, while the vibration amplitudesand mode shapes can be different for each individual blade inthe sector. Additionally, the vibration frequency as well asthe amplitudes and mode shapes are supposed to be known.</p><p>The aerodynamic analysis of freestanding blade cascade isperformed with twodimensional inviscid linearized flow model.As far as feasible the study is supported by non-linear flowmodel analysis as well as by performing comparisons againstavailable experimental data in order to minimize theuncertainties of the numerical modeling on the physicalconclusions of the study.</p><p>As has been shown for the freestanding low-pressure turbineblade, the blade mode shape gives an important contributioninto the aerodynamic stability of the cascade. During thepreliminary design, it has been recommended to take intoaccount the mode shape as well rather than only reducedfrequency. In the present work further investigation using foursignificantly different turbine geometries makes these findingsmore general, independent from the low-pressure turbine bladegeometry. The investigation also continues towards a sectoredvane cascade. A parametrical analysis summarizing the effect ofthe reduced frequency and real sector mode shape is carried outfor a low-pressure sectored vane cascade for differentvibration amplitude distributions between the airfoils in thesector as well as different numbers of the airfoils in thesector. Critical (towards flutter) reduced frequency maps areprovided for torsion- and bending-dominated sectored vane modeshapes. Utilizing such maps at the early design stages helps toimprove the aerodynamic stability of low-pressure sectoredvanes.</p><p>A special emphasis in the present work is put on theimportance for the chosen unsteady inviscid flow model to bewell-posed during numerical calculations. The necessity for thecorrect simulation of the far-field boundary conditions indefining the stability margin of the blade rows isdemonstrated. Existing and new-developed boundary conditionsare described. It is shown that the result of numerical flowcalculations is dependent more on the quality of boundaryconditions, and less on the physical extension of thecomputational domain. Keywords: Turbomachinery, Aerodynamics,Unsteady CFD, Design, Flutter, Low-Pressure Turbine, Blade ModeShape, Critical Reduced Frequency, Sectored Vane Mode Shape,Vibration Amplitude Distribution, Far-field 2D Non-ReflectingBoundary Conditions. omain.</p><p><b>Keywords:</b>Turbomachinery, Aerodynamics, Unsteady CFD,Design, Flutter, Low-Pressure Turbine, Blade Mode Shape,Critical Reduced Frequency, Sectored Vane Mode Shape, VibrationAmplitude Distribution, Far-field 2D Non-Reflecting BoundaryConditions.</p>

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 152-157).

Thesis (Ph.D.)--University of Wyoming, 2008. / Title from PDF title page (viewed on June 28, 2009). Includes bibliographical references.

Thesis (Ph. D. in Aeronautical and Astronautical Engineering)--Naval Postgraduate School, June 2003. / Dissertation supervisor and advisor: E. Roberts Wood. Includes bibliographical references (p. 205-210). Also available online.

This research presents a new, more efficient computational scheme for complex periodic flows, and brings forward two novel ideas. The first consists in the use of a Fourier space time representation in conjunction with a high-order spatial discretization. The second is based on the efficient treatment of the resulting set of equations using a fast, implicit solver. This thesis describes the formulation and implementation of the proposed framework. Firstly, a high-order spectral difference scheme for the Euler equations is introduced. Secondly, the non-linear frequency domain method resolving the unsteady behavior of the flow is discussed. Thirdly, a mathematical and experimental validation of the proposed algorithm is carried out. Numerical experiments performed in this thesis suggest that the methodology could be an attractive new avenue for large scale time-dependent problems, alleviating the computational cost traditionally associated with such simulations.

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